{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Equivalent Kernel"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The equivalent kernel for an estimation of a linear regression takes the form\n",
    "\n",
    "$$\n",
    "    k(x, x') = \\beta{\\boldsymbol \\phi}(x){\\bf S}_N{\\boldsymbol \\phi}(x')\n",
    "$$\n",
    "\n",
    "Where\n",
    "${\\bf S}_N = (\\alpha{\\bf I} + \\beta{\\boldsymbol \\Phi}^T{\\boldsymbol \\Phi})^{-1}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from numpy.linalg import inv\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z): return 1 / (1 + np.exp(-z))\n",
    "\n",
    "def gaussian_kernel(x, mu, s): return np.exp(-(x - mu)**2 / (2 * s ** 2))\n",
    "def sigmoid_kernel(x, mu, s): return sigmoid((x - mu) / s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.linspace(-1, 1, 200)\n",
    "s = 0.3\n",
    "alpha, beta = 1/2, 1\n",
    "mus = np.linspace(-1, 1, 12)\n",
    "\n",
    "xv = [-0.75, 0, 0.65]\n",
    "def plot_eq_kernel(x, xv, kernel, mus, s):\n",
    "    fig, ax = plt.subplots(len(xv), 1, figsize=(12, 7))\n",
    "    for axi, xi in zip(ax, xv):\n",
    "        xi = np.array([xi])[:, np.newaxis]\n",
    "        phi = kernel(xi, mus[np.newaxis, :], s)\n",
    "        phi_prime = kernel(x[:, np.newaxis], mus[np.newaxis, :], s)\n",
    "        SN = inv(alpha + beta * phi_prime.T @ phi_prime)\n",
    "        axi.plot(x, beta * phi_prime @ SN.T @ phi.T)\n",
    "        axi.grid(alpha=0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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eONaJcdbaF4AXAMaOHWvT09Pdj7QdeGq/HcFay0NzlxIZGsjPLx5DdFhQu++jI/OVDnx/n+GJuTnk14dzSr+EDttXZ+lKx1dnUL7cp5y5R/lyj/LlHuXLPd6er/YY/rEbaNpNmAI0v+zdt22MMQFAFFCGs0f7cWNMHvBD4CFjzN3tEJO0wmfZRXy9rZT7zurfIQV1Z7hlUibpcWH88oON1DY0ejocERER6abao6heDvQzxmQYY4KAK4BZzdrMAq5z3Z4BLLBOp1hr06216cBTwO+stc+2Q0xyDLUNjfxu9ib694zgqnFpng7nuIUE+vPIBUPYXnKQFxdq7moRERHxjDYX1dbaBuBu4FNgE/CWtXajMebXxpgLXM3+iXMMdS5wH/Cdafekc/17cR47S6v5+bTBBPj79nTlpw1IZMqQXjy7IJe9FTWeDkdERES6ofYYU421djYwu9myXzS5XQNceoxtPNIescixVVTX89znuUwekNAlxiEDPDR1EAs2F/Onz7bwp0tHeDocERER6WZ8u4tSjsvfvtpGVW0D908Z6OlQ2k1aXBg3TEzn3VW72bCnwtPhiIiISDejorqbKaqs4aXFO5g+MplBvSM9HU67uuv0LGLCgvjNR9lYqystioiISOdRUd3NPD1/K40Oy71n9vd0KO0uMiSQe8/qz9IdZXyWXeTpcERERKQbUVHdjewoOciby/O5alwaaXFhng6nQ1x5Qir9EiP4/exN1Dc6PB2OiIiIdBMqqruRP8/NITjAj7tP7+fpUDpMgL8fD04dSF5pNW8uzz/2A0RERETagYrqbmLL3io+WlfA9Selk9Aj2NPhdKjJAxIZ2yeGZ+Zv5VCdLggjIiIiHU9FdTfx9PwcwoMCuHVSpqdD6XDGGH567kCKq2r599d5ng5HREREugEV1d3ApsJKZq/fy40T0332cuTuOiE9lskDEnj+i1wqqus9HY6IiIh0cSqqu4Gn522lR0gAN53c9Xupm/rJOQOprGng719t83QoIiIi0sWpqO7iNhZUMGfjXm6cmEFUWKCnw+lUg5MiuXBkEi8tzqO4UpcvFxERkY6jorqLe3reViJDArjx5AxPh+IR953Vn/pGB39ZkOvpUERERKQLU1HdhW3eW8ln2UXcMDGDqNDu1Ut9WJ+4cK4Yl8rry3axq7Ta0+GIiIhIF6Wiugv76+fbCA/y54aJ6Z4OxaN+cHo/AvwNf567xdOhiIiISBelorqLyis5yEfrCrjmxD7dZsaPI0mMDOGGiRl8sLaATYWVng5HREREuiAV1V3U819sI9Dfj5u72YwfR3L7pL70CA7gT5+qt1pERETan4rqLmhP+SHeXbWbK05I7fJXT2ytqLBAbj+tL/M3F7Ny535PhyMiIiJdjIrqLuiFL53zMt96al8PR+Jdrj8pnfiIII2tFhERkXanorqL2VdVyxvL87l4dDLJ0aGeDserhAUFcOdpWSzOLeXrbSWeDkdERES6EBXVXcyLi7ZT3+jgjtOyPB2KV7pqfBq9IkP482c5WGs9HY6IiIh0ESqqu5Dy6jpeXbKTacOTyIgP93Q4Xikk0J+7T89ixc79fJmzz9PhiIiISBehoroLeWlxHgfrGrlrsnqpj+aysamkxITy57nqrRYREZH20S5FtTFmijFmizEm1xjzQAvrg40xb7rWLzXGpLuWn2WMWWmMWe/6fXp7xNMdHaht4N9f53HW4J4M6NXD0+F4taAAP+45ox/rdlcwN7vI0+GIiIhIF9DmotoY4w88B5wLDAauNMYMbtbsJmC/tTYLeBJ4zLW8BDjfWjsMuA54pa3xdFevfrOTikP13K1e6la5aFQymfHh/HluDg6HeqtFRESkbdqjp3ockGut3W6trQPeAC5s1uZC4D+u2+8AZxhjjLV2tbW2wLV8IxBijNHEym6qqW/kxYU7OKVfPCNSoz0djk8I8PfjnjP7sXlvFR+vL/R0OCIiIuLjAtphG8lAfpP7u4HxR2pjrW0wxlQAcTh7qg+7BFhtra1taSfGmFuBWwGSk5PJy8trh9DdU1pa2un7bI3/biil5EAtlwzq7ZG8HIm35uuwYVGWjNhgHv9kI4N61BLgZzwaj7fny9soX+5TztyjfLlH+XKP8uUeX8hXexTVLVUizb9PP2obY8wQnENCzj7STqy1LwAvAIwdO9amp6e7HWh78NR+j6SuwcHbr29jbJ8YLjxxMMZ4tjBsztvy1dxPp4Zy+6srWbM/kBljUjwdjtfny9soX+5TztyjfLlH+XKP8uUeb89Xewz/2A2kNrmfAhQcqY0xJgCIAspc91OA94BrrbXb2iGebuW91bsprKjhrtOzvK6g9gXnDOnJ0ORInp6fQ32jw9PhiIiIiI9qj6J6OdDPGJNhjAkCrgBmNWszC+eJiAAzgAXWWmuMiQY+Bh601i5uh1i6lYZGB89/sY2hyZGc1j/B0+H4JGMMPzprAPllh3h7xW5PhyMiIiI+qs1FtbW2Abgb+BTYBLxlrd1ojPm1MeYCV7N/AnHGmFzgPuDwtHt3A1nAz40xa1w/iW2Nqbv4eH0heaXV3D1ZvdRtcdqABEanRfOXBVupqW/0dDgiIiLig9pjTDXW2tnA7GbLftHkdg1waQuPexR4tD1i6G4cDstfP99Gv8QIzh7cy9Ph+DRjDD8+ewBXvbiU15ft4oaJGZ4OSURERHyMrqjooz7L3suWoirumpyFn4dnregKTsqK58TMOJ77fBuH6tRbLSIiIu5RUe2DrLU8PT+XzPhwzh+R5Olwuowfnd2fkgO1vLwkz9OhiIiIiI9RUe2D5mYXsamwkrsmZ+GvXup2MzY9llP7J/D8l9uoqqn3dDgiIiLiQ1RU+xhrLc8s2EpabBgXjlQvdXv70dn9Ka+u5x9fbfd0KCIiIuJDVFT7mM+3FLNhTyV3T84iwF9/vvY2PCWaacN784+FOyiurPF0OCIiIuIjVJX5kMNjqVNiQrlodLKnw+myfnLOABocDp6ct9XToYiIiIiPUFHtQ77aWsLa/HLumpxFoHqpO0yfuHCuHt+Ht1bkk1tc5elwRERExAeoMvMR1lqenpdDUlQIl4xO8XQ4Xd73T88iNNCfx+Zs8XQoIiIi4gNUVPuIxbmlrNpVzh2TswgK0J+to8VFBHP7qZnMzS5ieV6Zp8MRERERL6fqzAc4x1Ln0CsyhMvGqpe6s9x0ciY9I4P53exNWGs9HY6IiIh4sXa5TLl0rG+2l7E8bz+/umAIwQH+ng6n2wgN8ufeM/vzwH/X8+nGvUwZ2tvTIXUbDodlb2UNFYfqqTxUT3VdI8EBfoQG+dMjJICUmDBPhygiIvI/VFT7gGfmbyWxRzCXn5Dq6VC6nRljUnhx0Q4en7OFMwb11AmiHaS4qoYvt+xj2Y4ythRVkVNURU2944jtjYHE8ED69y5iVFoMEzJiGZUWQ2iQPnSKiIhnqKj2cotzS1iyvZSfTxtMSKAKhs4W4O/HA1MGcvPLK3hjeT7fm9DH0yF1GUWVNbyzcjcfrysku7ASgLjwIAb1juSqcX3omxhObFgQUaGBhAb5U9vg4FBdI5U19eSVVLN+ZxEFB+p4dsFWnrEQ6G+YmBXP1GG9OWdwL6LCAj38DEVEpDtRUe3FrLU8/ukWkqJCuHp8mqfD6bbOGJTIuPRYnp6Xw0WjkokI1svmeFlr+XpbKS8tzuPzLcU0Oixj+8Rw/5QBnNo/gcG9IzHGtGpbeXmBpKenU1lTz8q8/SzOLeGTDXu5f8s6fua/nrMH9+LqCWmcmBnX6m2KiIgcL1UHXuzTjUWszS/n8UuGq5fag4wxPDh1IBf99Wue/yKXn5wz0NMh+RxrLV/m7OOZ+VtZtauc+Ihgbp2UyWVjU8mID2/TtiNDApk8MJHJAxP52XmDWLe7gllrC3h31W4+Xl9I34Rwbjo5k0vGJOucBBGRVnA4LDtKD7KxoJKdJQcpP1RPeXU9tQ2NRIUGEhMWRGJkMKNSYxjUu4eu8OyiotpLNTosf/psC30TwrlYV0/0uFFpMUwfmcQ/vtrBZWNT6RPXtkKwO9mwp4JffbiR5Xn7SY4O5TfTh3LpmJQO+aBojGFEajQjUqP5yTkD+GhdIS8vyeOh99bz9Pwcbjklk6vGpxEWpLc+Tyk5UMvmwiry91dTUH6IgvIaKmvqqa5r4GBtI8ZAoL8fwQF+RIYGkhARTGJkMKkxYWQlRpARH65OBpEOkF9WzYLNxSzYXMzyvDKq6xq/XRce5E90WBBBAX5UHKqnvLoOh2tSrLAgf8amx3LpmBTOGdKrW0/7q/8sXuq/q3aTW3yA568erU+AXuLBqYOYm13Ebz7axIvXjfV0OF6v9EAtf/psC28szyc2LIjfXTSMGWNSOu0NNyTQnxljUrhkdDKLc0t57vNcHv14Ey98tZ37zurPjDEpem11sEaHZcOeCpZsL2XZjjI27KmguKr22/V+BnpGhhAdFkS4a2YXgLoGBwdqG9iz/xBfVtVyoLbhfx6TlRjB6LQYRveJYXxGrD7kehmHw1JYWcPOkoMUVdVQdrCe/QfrOFjXQKPD0uiw+PsZwoMDiAgOICo0kKToEHpHhZISE0qPEJ0P0VnKq+v4YE0Bb6/MZ8Me57ktGfHhXDI6hWEpUQxJiiQrMeI73/IdnqFp5c79rMgrY8GWYr7/+mriI4K5alwqN0/KJLIb/h1VVHuhmvpGnpq3leEpUUwZ2svT4YhLz8gQvn9GP/7wyWa+2FLMaQMSPR2SV7LW8tG6Qn7xwQaqahq4cWIGPzijH1GhnnmDNcZwcr94Tu4Xz4q8Mn43exMP/Hc9/1q8gwfOHcjkAYkac92ODtQ28OWWfXyWvZfPNxdTWeMsiDMTwjk5K57BSZEM6h1Jenw4PXsEt+qDTXVdAztLq9lafICtRVWs31PB7PWFvLE8H4D0uDAm9U9g8sBEJvaN79Y9ZZ2tvtHBhj0VrM0vZ8mWAnZW7mL7voPUNf7v7D1+BsKDAvD3N/gbQ6O1HKxtoL7xu9cASI4OZUCvHgzq3YMxfWIYkxarE4/b2Zr8cv61aAdzNuylrtHBkKRIHj5vEGcM6tmqIXl+foak6FCSokM5f0QSv3RYvty6j1eX7OQvn+fy+vJ8Hj5vEBeMSOpW768qqr3QvxbvYE/5If44Y3i3Ohh9wY0TM3hreT6//jCbk/TP+zv2VdXy8/c3MGfjXkakRPHHS0fQv2cPT4f1rbHpsbx7x0l8unEvj83Zwo3/XsGEzFgemjqI4SnRng7PZ9U3Oli4dR/vrtrD3Owi6hocxIYHcc6QXpzSP4EJGbEkRoYc9/bDggIY1NtZjB/mcFi2lxxgcW4pX+bs4+0Vu3l5yU56hARw1uCenD88iVP6xevbiHZmrWXbvgPM31TM19tKWZFXxkHXMIGYUH9GpMVyav8E+sSF0ycujN5RIcSGBxEZEoif33f/n9U2NLL/YD0FFYcoLK8hr/QgOUVVbC6s4sucfTS6xhgM7NWDSf0TOK1/AmPTY/XeexystXyWXcQLX21n5c799AgO4KrxaVw2NpXBSZHH3sBR+PkZJg9IZPKARNbtLufn72/gnjfW8MayfJ64bARJ0aHt9Cy8m/HFK8WNHTvWrlixotP3m5eXR3p6eofuo7iqhsl//IKTsuL5x7W+PcSgM/LlCV9sKeb6l5bzk3MGcNfkrHbbrq/n68ucffzorTVUHmrg3rP6c8spGR1a0LQ1X/WNDl5ftoun5m2l7GAdF41K5oFzB9KzDcWft2vvYyy/rJqZy3bx9op8Sg7UERsexAUjkjh3aC/Gpsfi30IR1VFq6htZnFvC7PV7mZu9l8qaBnpGBnPJ6BQuPc4TYn39NdlerLWsyS/nw7WFzNtUxK6yasA5DOfEzDgmZMYxpk8Mh8oKycjIaLf9HqprZE1+OSvyyliyvZTleWXUN1oigl0fnEb05uSsBJ8tsDvr+LLWMm9TMU/OzSG7sJLU2FBuOCmDS8emdNhQm0aH5fVlu/jDJ5sJCfTn798bzZg+sW3apqdej8aYldbaVhVk6qn2Mk98mkNdo4OHpg7ydChyBKcNSOTcob14Zv5WzhvWm/Q2zl7h6+obHfzpsy38/cvt9O8ZwWvQjfKOAAAgAElEQVQ3T2BAL+/pnT6SQH8/rj0xnYtGJfP8F9t4ceEOPtu4l3vO7Mf1J2X47D/qjmatZcn2Ul5cuIPPtxRjgDMH9eTSsamcNiDBYxdICgn054xBPTljUE/qGoaxYHMxb6/I529fbuOvX2xjXEYsl41NZeqwXjpRtZVyi6v4YE0BH6wpYFdZNUH+fkzMiuPWSZmcPjDxO72Pefvb90NUaJA/J/aN48S+cXz/jH4crG1gybZS5m0q4pMNe3lv9R6iwwI5d2gvzh+RxPiMuE79IOftrLUs2FzMU/O2sn5PBX3iwnji0hFcODKpw7/B8fczXDOhD+MzYrnl5RVc+cJSHp0+lMu6+EXs2qWn2hgzBXga8AdetNb+odn6YOBlYAxQClxurc1zrXsQuAloBH5grf30WPvrqj3VG/ZUcP6zi7j55Ax+dt7gDttPZ+nKvTxFlTWc+cSXDE+N4tWbxrfLMB1fzNfeihrufG0lq3aVc/X4tE69SFF75yuv5CC/+Sib+ZuLyUwI55HzhzCpf0K7bd8btCVnDodl/uZinvs8lzX55d+ekHTFuDSv/mq3qLKGd1ft5u0Vu9lRcpAewQFcMiaFayb0ISsx4qiP9cXXZFuVHKjlvVV7eH/NHjYWVOJn4KS+8VwwMolzhvQ66rkRnZmvugbnkKNZawuYm11EdV0jiT2CmTEmhSvHpZEaG9YpcbRFR+XLWssXOft4am4Oa3dXkBobyvdP78fFo5I9MhyqvLqOu2euZlFuCT+dMpA7Tut7XNvpFj3Vxhh/4DngLGA3sNwYM8tam92k2U3AfmttljHmCuAx4HJjzGDgCmAIkATMM8b0t9Y20s1Ya/nNR9nEhAVx9+n9PB2OHEPPyBB+eu5AHn5/A++u2sOMMSmeDqnTfbO9lLtnruJQXSPPXjWKacOTPB1Sm6THh/PP609gweYifvVhNtf+axnnDOnJw+cN9ol/0B2lodHBR+sKef6LbWwpqiIlJpRHpw9lRgdNi9jeekaGcOdpWdxxal+W5+1n5tKdzFy6i39/ncfErDi+NyGdMwclduux1w6H86JMry/bxWfZe6lvtIxIieIX0wYzbXjvNo2H7yhBAX7ffjNxqK6R+ZuLeG/VHv725Tae/3Ibp/RL4OrxaZwxsPv8ba21LNxawpPzcli9q5zk6FD+cPEwLhmT4rFvkACiw4L49w0ncN9ba3lszmZCA/24fmL7DRPyJu3xHdg4INdaux3AGPMGcCHQtKi+EHjEdfsd4Fnj7Nq7EHjDWlsL7DDG5Lq2t6Qd4vIps9YWsHRHGY9OH+qxWRLEPVeNS+P91Xt49ONsThuQQHxEsKdD6hTWWl5anMdvZ2+iT2wYr98ygX5edDJiW50+sCcn9Y3nn4t28OyCXM7c8iV3npbFbadm+kQR2V5q6ht5d9Vu/v7ldnaVVdO/ZwRPXT6SacN7+2SRYoxhXEYs4zJieXhaLW8uz+e1b3Zy+6srSYoK4arxaVx+QhoJPbrH6xic5/C8vWI3by7PZ1dZNdFhgVx7YjpXnJDqU6/p0CB/pg1PYtrwJArKD/Hm8nzeWL6L215ZSc/IYC4fm8rl49JI9uJvVNri8JVqn5ybw4qd+0mKCuG3Fw3l0jGpXjOMLcDfjycuG0FtQyOPfJhNSKA/V4zreleKbo+iOhnIb3J/NzD+SG2stQ3GmAogzrX8m2aP7XZXOtl/sI5ff5jNyNRoruyCB1lX5edn+P3Fw5j6zEJ+/v4G/nr16C4/W0tdg4NfztrA68vyOWtwT/582YguOadsSKA/d03O4qJRyfx29iaenJfD2yvz+cW0wZw1uGeX/jsfrG1g5tJd/GPhdoqrahmRGs3D5w3izEE9W5y9wRfFRwRz1+QsbpuUyfzNxbyyZCd/+iyHp+dv5dyhvbn2xD6M6RPj6TA7RKPDsnDrPl5ftov5m4ppcFgmZMbyo7P7c86QXj7/wTEpOpR7z+rP90/PYsHmYmYu28VfPs/l2c9zmTwgkavGp3HagMQuMfbaWss328t4cl4Oy3aU0SsyhN9MH8plY1O88uqxgf5+PHPlKG57ZSUPvree6LBApgzt7emw2lV7FNUtHZnNB2ofqU1rHuvcgDG3ArcCJCcnk5eX50aI7aO0tLRDtvvY53soP1TH4xNSyd+1s0P24QkdlS9vEgjcMDaBF5bu5R9z13J2/+Ofls3b81VR08AvP8tnTUE114yK58ZxcZTu3YOnou6sfP3kpFjO7BPM04sKufWVlZyQGsH3J/YiLdr3ejSPlrOKmgb+u76M/24oo6q2kdHJ4fz01F6MTg7HmBp2daH3pqYGhMOjZ/Zk19hoPthYxpxNe5m1toC+cSGclR7EhfUOQgO9o7evLfZW1TFnSzmfbC6n6EA9USH+XDIslvMGxbiO5Xr27sk/5naOxtvew/qHwyOTEykcE83Hm/Yze0sZ8zcXkxgRyHkDozl3YAyJEZ7rFDjefDmsZXFeFa+vKSG76BBxYQH8YGIvzhsUQ3CApXB32/6OHe3BU+Ip2n+Ae99cQ2h9JX1iWvde6m3HV0vafKKiMeZE4BFr7Tmu+w8CWGt/36TNp642S4wxAcBeIAF4oGnbpu2Ots+udKLi17klXPXiUu48rS/3TxnYrtv2tO5ykk+jw3LFC0vYXFjFnHsnHfdXjN6cr9ziA9z0n+UUltfw2IxhXDTK82PIOztf9Y0OXl6yk6fm5lDT0MiNEzO4c3KWTw3XailnRZU1vLhwO68t3UV1XSNnDurJnZP7Mjqta/bUHkt1XQPvry7g5SV5bN5bRY+QAC4dk8o1E9LITDj6iY3epqa+kbnZRby1Ip9FuSVYCydnxXPFuFTOGtyz3Xszvfk9DJyv4XnZRcxctouFW0vwM87hXleNT+XU/p3fe+1uvuoaHLy/Zg9//3Ib2/YdJDU2lFtPyeTSsak+9w1DYcUhpj2ziOiwQD64+2Qigo/dx+sLJyq2R1EdAOQAZwB7gOXAVdbajU3a3AUMs9be7jpR8WJr7WXGmCHATJzjqJOA+UC/Y52o2FWK6pr6Rs59eiHWWub8cJLPvSiOxdvfYNtTflk1U576imEpUcy8ecJxfU3urflauHUfd762iiB/P164dkyb5xptL57K176qWh6fs5l3Vu0mMiSQuydn8b0T+/jE67dpzvJKDvL3r7bz7srdNDgcXDAiiTtOy/KJ6RA7g7WWD7/JZm5eHZ+sL6TBYTmlXzyXjk3l7ME9vfbv7XBY1uwuZ9aaAt5bvYeKQ/UkR4cyY0wKM8akdOhJt976HtaSXaXVvLF8F2+t2E3JgVqSokK4ZEwKF4xI6rTx5K3NV3l1HW+v2M0/F+1gb2UNg3pHcsdpfZk6tJdPnt9w2NfbSrjmxaVMGdqL56469vBJXyiq2zz8wzVG+m7gU5xT6v3LWrvRGPNrYIW1dhbwT+AV14mIZThn/MDV7i2cJzU2AHd1p5k/fvvxJnaUHGTmzeO99g1aWic1NoxfXjCE+99ZxwsLt3P7qcc3ZZC3eXlJHr/6MJt+iRG8eN1YUmK67ywYhyX0COaPl47ghokZ/GHOZn47exMvLd7BXadnedWJQS1xntBUwr8W5TF/cxGBfn7MGJvCbZMy6RPXvedbb84Yw/De4Vxw4hCKpw3ijWX5vL5sFz94fTURwQGcO7QX00YkcWJmnMf/5g6HZeWu/cxeX8icDXsprKghKMCPc4b04rKxKUzsG99lxsO3l7S4MO6fMpAfntmf+ZucvdfPfZ7LXxbkMrBXD84fkcQFI5I8NvOPw2FZsXM/ry/bxcfrC6lrcDAhM5bHZgxnUr/4LnFex0l94/nplIH8/pPNvLxkJ9edlO7pkNpMV1R0Q3t+SpqzYS+3v7qSWydldtkLvfhSr0V7sNZy98zVzNm4l9duHs+EzDi3Hu9N+WpodPDrj7J5eclOzhiYyNNXjmrV13OdyVvytWhrCU/M3cLqXeUkRYVwx2l9mTEmldAg7/mgXNvQyIdrC/nbgi3kltYQGx7E1ePT+N6EPl45XZq3aH6MORyWb7aX8t7qPXyyYS8HahuIDAngzEE9mTwwkZOz4okJD+qU2KrrGli2o4zPNxfzyYa9FFfVEhTgx6n9E5g6rBdnDOpJZCefROwtr8njVVxVw+x1hXy4rpCVO/cDMCotmnOH9uK0AYn0S4xo12K2peNr/Z4KPl5fyEdrCyioqKFHcADTRyVzxbhUhiRFtdu+vYW1lutfWs6yHWV8+sNJpMUd+UOML/RUq6h2Q3v9QfeUH2Lq0wtJiw3j3TtO8ngvR0fx9TfY43GgtoELn11ExaF6Pvr+KfSKan3B4i35qjhUz90zV7Fwawm3Tsrkp1MGeuWZ8t6SL/j/+WGfmpfDql3lxIQFcvX4Plx7omeL1vyyat5euZuZS3dRcqCW9Jhgbp/cn+mjkvXtWCsc7RirqW9k0dYS5mzcy9zsIioO1WMMDE+JZnxGLKNSoxndJ6bdLntfeqCWNfnlrMkvZ9mOMlbt2k99oyU4wI/JAxI511VIe/LDrze9Jtsqv6yaj9YV8uHaArILKwHoHRXCxKx4xvaJYUyfGPomRLTpG4DtO3ZgeiSyaud+Fm7dx6LcEkoO1BHobzilXwLThvdmytCufwXQgvJDnP3kVwxLjmLmLUe+mJqK6g7iy0V1Q6ODq/6xlI0FFXz0g1PI6MKXuO5Kb7DuyC2u4oJnFzOodySv3zKh1R+avCFf2/Yd4NaXV7CztJrfXjSUy0/w3ikevSFfzVlrWbajjH8u2sHcTUX4G8PkgYnMGJPC6QMTO+UCDPsP1jF3UxH/XbWbb7aXYQyc2j+Bm07OICXgABkZXfOiCx2htcdYo8Oydnc5C3NKWLh1H+t2V1DX6AAgLjyIvokRZCVGkBoTRmKPYBIjg4kKDSQ4wJ8Q18witQ0OausdVNbUU1xVQ3FlLbv3H2LbvgPkFh+guKoWAD8Dg3pHcnJWPBOz4jkhPdZrvhXxxtdkeygoP8RXOfv4Yss+luWVUXawDoCwIH/6JUaQldiDjPgwEnuEkNAjmOiwQIIC/Ajy98MYOFDbyIGaBsoP1ZFfdoj8/dXs2HeQdbv3c7Du/4+Tk/vFc0q/BM4clEh0WOd84+EtZi7dxUPvree3Fw3l6vF9WmzjC0V11/7442Wstfzqw2yW5ZXx58tGdOmCujvLSuzB4zOGc/fM1fxy1kZ+d9FQnxj/Nn9TET98Yw2BAX68ehzDV8Q5Dnd8ZhzjM+PYWXqQmUt38d/Ve5ibXURMWCCnD+zJWYMTOaVfAuHt1KNorWXbvgMszi1lbnYRS7aX0uiwpMeF8eOz+3PR6JRvZ6TJyzvYLvuU/+XvZxidFsPotBjuObMftQ2NZBdUsnpXOVv2VpG77wAfryuk4lC9W9vtERJA34QIJvVPoH/PCEamxjA0ObLL91x6m6ToUK4Yl8YV49Kw1pJXWs2KvDI2FlSSW3yARbn7eHdVbau3FxMWSFpcOGdkRTFxUArDU6IZ0LNHtx73fuW4VD5eX8DvZ2/mtAGJPnuhHr0yO9ELX23nlW92cuukTC4e7fkpyaTjTBuexMaCSp7/YhtJUSF8/wzvvfS8w2F57vNc/jwvh8G9I/n798bohMR20CcunAenDuIn5wxg4dYSPlizh3mbinh31W4C/Q2Dk6IYkxbDqLRoshIj6BMXdsxiqdFhKa6qIafoANkFlWwoqGDZjjL2uXoxM+PDuW1SJucO7c3Q5Eif+DDXFQUH+DMqLYZRzaYlPFjbQHFVLUWVNRyoaaC2wUFNfSPGOB8THOBHREgAiT2CSegRTERwgP6GXsYYQ0Z8OBnx4VzaZHlNfSP7qmrZd6CW8uo66hst9Y0OHBZ6BAcQHhxAVGggyTGh3w7Rcfa8eu+3gZ3JGMMfLh7O2U9+xaMfZfP8NWM8HdJxUVHdSWatLeD3n2zmvOG9eaCLzUctLbv/nAEUVdTwxNwcEiODvXIoxYHaBn781lrmbNzLRaOS+f3FwzTWtp0F+PsxeWAikwcm0tDoYMXO/XyxZR+rdu7ntaU7+dfiHd+2TegRTExYID1CAgkPDsDhsNQ1OKhtcP7DLqqqpdHx/0P2kqNDOTEzjpP6xnFS33hSY0NVhHmx8OAAMoID9C1lFxQS6E9qbJjHZgvpClJjw7j91L7fXiFyXIZ3TN/qDhXVnWDB5iJ+/NZaxqXH8sSlI7r1VzzdiTGGx2YMZ9+BWh56bwOx4cGcNbinp8P6Vl7JQW55eQXbSw7y8HmDuOnkDBVkHSzA348JmXHfDq2pa3CQU1RFXulBdpZWs6u0mopD9VTV1lNxqB5/A0EBfkSHBZGV2IPeUSH0jAqhX2IEg3pFEhXmOxeeERE5llsnZfL6sl385qNsPrhros/VSyqqO9ir3+zkFx9sYEhSFC9cO0a9gN1MoL8fz18zhqv+8Q13vraSpy4fxXnDe3s6LGavL+SBd9fh52d4+cZxTMyK93RI3VJQgB9Dk6MYmtz1psoSEXFXaJA/908ZwH1vreW91Xu4ZIxvDZXtmnO5eQGHw/KHTzbz8PsbmDwgkTdundDtzuYVp4jgAF69eTwjU6P5/uureGt5vsdiqa5r4IF313Hna6vIiA/nw7tPVkEtIiJeY/rIZIanRPH4p5uprmvwdDhuUVHdSlU19f8zlvFo1uaXc8nfvuZvX27j6vFp/P17Y9rtTH/xTZEhgbx843gmZsVz/7vr+NuX2+js6SxX7ixj2l8W8eaKfO48rS/v3HGSxv+JiIhX8fMz/HzaYIoqa3lx4Y5jP8CLqNJrpSc+y2H2uj1878QGLj8h9TsXdHA4LNmFlfzn6zzeXrmb+Ihgnrh0BBePTtY4VQGcX2u9eN1Y7ntrLX/4ZDOrdu7nj5eOICq0Y8fFVtXU8/icLby6dCdJUaG8dvN4Tuqr3mkREfFOJ6THcuagnry4cDvXT0zv9KuDHi8V1a00qX88G3bt44m5OTw9fytj02OIiwgmMiSAqpoGvt5WStlB55WQbpuUyd2nZ9HDRw4C6TzBAf48e+UoRqfF8PvZm5j2l4U8e+VoRqRGt/u+Gh2W91fv4Y+fbqGoqobrT0rnx2cP0LcmIiLi9e45ox/nP1vEy1/ncffp3jstbVP679pKpw/sSWbIIYhIYOayXSzdUcamgkoqaxoI8DOc2j+BU/rFc3K/eBJ7eO6yxOL9jDHcdHIGI1OjuXvmKqb/dTGXj03lskFhpLfD9q21LNhczONztrClqIphyVE8f83o78yZKyIi4q2GpURx+sBEXly0g+sn+saVYFVUuyk9PpyHpg7ydBjSBYzpE8OcH07iL/O38u+v85i1xnDbqZYrxqXSM9L9D2ZVNfW8t3oPryzZydbiA6THhfHsVaOYOrS3z01LJCIi8oMz+jH9ucW8vCSPqeneX7J6f4QiXVhUaCAPTxvMVePTePidVTw5L4en5+dw+sBELhiZzOi0aJKjj3xBjz3lh/gqZ9+3PwfrGhmeEsUfZwxn+qhkAv11LrKIiPimkanRnNo/gRcX7uC05ExPh3NMKqpFvEBmQgS/OzcNIhJ4a0U+b6/czbxNxQDEhQeRlRhBWJA/IYH+NDosu/cfIn9/NVU1zumGekeFcMHIJC4/IY2RHTA+W0RExBN+cEY/Lnn+a2Zt3M9gLx9araJaxIukx4dz/5SB3HdWfzYVVrFmdznr8svJKz1IyYE6auobMcZ5eeoxfWLIiA/nlH7xZCVGaJYZERHpcsb0iWHqsF74mc6dhvZ4qKgW8UIB/n4MS4liWEoUTOjj6XBEREQ85q9XjyEvL8/TYRyTBlyKiIiIiLSRimoRERERkTZSUS0iIiIi0kbGWu8f+N2cMWYfsNMDu44HSjywX1+lfLlH+XKP8uU+5cw9ypd7lC/3KF/u8VS++lhrE1rT0CeLak8xxqyw1o71dBy+Qvlyj/LlHuXLfcqZe5Qv9yhf7lG+3OML+dLwDxERERGRNlJRLSIiIiLSRiqq3fOCpwPwMcqXe5Qv9yhf7lPO3KN8uUf5co/y5R6vz5fGVIuIiIiItJF6qkVERERE2khFtYiIiIhIG6mobsYYc6kxZqMxxmGMOeLULcaYKcaYLcaYXGPMA02WZxhjlhpjthpj3jTGBHVO5J5hjIk1xsx1Pd+5xpiYFtpMNsasafJTY4yZ7lr3b2PMjibrRnb+s+g8rcmXq11jk5zMarJcx9d324w0xixxvW7XGWMub7KuWxxfR3o/arI+2HW85LqOn/Qm6x50Ld9ijDmnM+P2lFbk6z5jTLbreJpvjOnTZF2Lr82urBX5ut4Ys69JXm5usu461+t3qzHmus6N3DNaka8nm+QqxxhT3mRddzy+/mWMKTbGbDjCemOMecaVz3XGmNFN1nnX8WWt1U+TH2AQMAD4Ahh7hDb+wDYgEwgC1gKDXeveAq5w3f4bcIenn1MH5+tx4AHX7QeAx47RPhYoA8Jc9/8NzPD08/C2fAEHjrBcx9d32/QH+rluJwGFQLTrfpc/vo72ftSkzZ3A31y3rwDedN0e7GofDGS4tuPv6efkBfma3OQ96o7D+XLdb/G12VV/Wpmv64FnW3hsLLDd9TvGdTvG08/J0/lq1v77wL+a3O9Wx5frOU8CRgMbjrB+KvAJYIAJwFLXcq87vtRT3Yy1dpO1dssxmo0Dcq212621dcAbwIXGGAOcDrzjavcfYHrHResVLsT5PKF1z3cG8Im1trpDo/Je7ubrWzq+Wn6+1toca+1W1+0CoBho1dWvuogW34+atWmax3eAM1zH04XAG9baWmvtDiDXtb2u7Jj5stZ+3uQ96hsgpZNj9CatOb6O5BxgrrW2zFq7H5gLTOmgOL2Fu/m6Eni9UyLzUtbar3B2th3JhcDL1ukbINoY0xsvPL5UVB+fZCC/yf3drmVxQLm1tqHZ8q6sp7W2EMD1O/EY7a/gu28gv3V9pfOkMSa4I4L0Iq3NV4gxZoUx5pvDQ2XQ8XXM48sYMw5n79C2Jou7+vF1pPejFtu4jp8KnMdTax7b1bj7nG/C2Ut2WEuvza6stfm6xPU6e8cYk+rmY7uSVj9n17CiDGBBk8Xd7fhqjSPl1OuOrwBP7txTjDHzgF4trPqZtfaD1myihWX2KMt92tHy5eZ2egPDgE+bLH4Q2IuzEHoB+Cnw6+OL1Du0U77SrLUFxphMYIExZj1Q2UI7HV//v53ewCvAddZah2txlzu+WtCa951u9Z51DK1+zsaYa4CxwKlNFn/ntWmt3dbS47uI1uTrQ+B1a22tMeZ2nN+KnN7Kx3Y17jznK4B3rLWNTZZ1t+OrNXzm/atbFtXW2jPbuIndQGqT+ylAAVCC82uJAFdv0OHlPu1o+TLGFBljeltrC11FTfFRNnUZ8J61tr7JtgtdN2uNMS8BP26XoD2oPfLlGsaAtXa7MeYLYBTwLjq+WsyXMSYS+Bh42PX14OFtd7njqwVHej9qqc1uY0wAEIXz69bWPLaradVzNsacifOD3anW2trDy4/w2uzKRc8x82WtLW1y9x/AY00ee1qzx37R7hF6F3deU1cAdzVd0A2Pr9Y4Uk697vjS8I/jsxzoZ5wzMQThfGHMss6R85/jHDcMcB3Qmp5vXzYL5/OEYz/f74wdcxVKh8cLTwdaPPu3CzlmvowxMYeHKRhj4oGJQLaOryPmKwh4D+eYu7ebresOx1eL70fN2jTN4wxgget4mgVcYZyzg2QA/YBlnRS3pxwzX8aYUcDfgQustcVNlrf42uy0yD2jNfnq3eTuBcAm1+1PgbNdeYsBzuZ/v6nsilrzesQYMwDnyXVLmizrjsdXa8wCrnXNAjIBqHB1mHjf8eXJsyS98Qe4COenn1qgCPjUtTwJmN2k3VQgB+cnyJ81WZ6J859SLvA2EOzp59TB+YoD5gNbXb9jXcvHAi82aZcO7AH8mj1+AbAeZ7HzKhDh6efk6XwBJ7lystb1+yYdX0fN1zVAPbCmyc/I7nR8tfR+hHOYywWu2yGu4yXXdfxkNnnsz1yP2wKc6+nn4iX5mud6/z98PM1yLT/ia7Mr/7QiX78HNrry8jkwsMljb3Qdd7nADZ5+Lt6QL9f9R4A/NHtcdz2+Xsc5a1M9zvrrJuB24HbXegM858rneprMzOZtx5cuUy4iIiIi0kYa/iEiIiIi0kYqqkVERERE2khFtYiIiIhIG6moFhERERFpIxXVIiIiIiJtpKJaRERERKSNfPKKivHx8TY9Pb3T91tXV0dQUFCn79dXKV/uUb7co3y5Tzlzj/LlHuXLPcqXezyVr5UrV5ZYaxNa09Yni+r09HRWrFjR6fvNy8vDE8W8r1K+3KN8uUf5cp9y5h7lyz3Kl3uUL/d4Kl/GmJ2tbavhHyIiIiIibeSTPdUiItI6tQ2NHKhpAKD8UAO1DY0EB/h7OCoRka5HRbWISBeyr6qW2esLWblzP5sKK9lecpBGh/12vb9fDpnx4QzqHcmYPjGcN7w38RHBHoxYRKRrUFEtIuLjHA7LnI17eWtFPgu3ltDosCRHhzKodw/OGdKLhB7BGAMlpaU4AiPYvLeSlTv3M2ttAb/+KJtT+sVz2dhUpgzphZ+f8fTTERHxSSqqRUR8lLWWL3P28ficLWQXVpIcHcptkzKZPiqZ/j17fKd9Xh7/c6JPTlEV76/ewwdrCrjztVUMSYrk/ikDmdQvHmNUXIuIuENFtYiID9q9v5oH3l3PotwSUmNDeerykVwwIsmtnub+PXtw/5SB/PjsAcxaW8ATc7dw3b+WcXJWPH+4ZBgpMWEd+AxERLoWFdUiIj7EWst7q/fwyw82YoFHzh/MVeP7EBRw/JM5+fkZpo9KZuqw3sxcupM/fZbDuU8t5NfThzB9ZLJ6rUVEWkFFtYiIj6iua+Cn767nw7UFjO0Tw5OXjyQ1tv16k4MC/Lh+YgZnDOrJvb6Fe+gAACAASURBVG+u4d4317Jg8z4eu2QYYUH6dyEicjR6lxQR8QHFlTXc9J8VbCyo4Cf/x959x0dVpY8f/5xJ7z2UJJBOSOiEKoqACFgAARUrll1117K79r7YVl3b/hR17XXXhoIoKKiIgiK9JAQCCUlIgfTekzm/PzL6jdkAGTLJnSTP+/XKi5l7z8x97sOZmWfunHvurCHcMDUKhy46qTDM352Prp/EyxvSePabg2QWVfPGkkSCvV27ZHtCCNEb2OTiL0qp2UqpVKVUmlLq7nbWuyilPrKs36KUCm+zfpBSqkopdbst4hFCiN7kwLEK5r/4E+mFVbx2ZSI3TovusoL6Vw4mxU3TY3j1ikTSCqq44KWfST1W2aXbFEKInqzTRbVSygF4EZgDxAOXKKXi2zS7FijVWkcDzwFPtln/HPBVZ2MRQojeZueRUi58eTPNWvPx9ZOYMbRft27/rPh+fHLDJBqbzSx6+Wd2HSnt1u0LIURPYYsj1eOBNK31Ya11A/AhMK9Nm3nAO5bby4EZynLmi1JqPnAY2GeDWIQQotfYnV3Gkje24u/pzIo/n8awEB9D4hgW4sPKG0/D39OZK9/Yyu7sMkPiEEIIe2aLMdUhQHar+znAhOO10Vo3KaXKgQClVC1wFzATOOHQD6XUdcB1ACEhIWRmZtogdOsUFxd3+zZ7MsmXdSRf1unt+TpQUMttX2bi4+rAU3NCaSjLJ7OTtWxnc/bUnFD+uiqDy17bzDPnhRMX7Na5gOxcb+9jtib5so7kyzo9IV+2KKrbG9inO9jmIeA5rXXVyaZs0lq/CrwKkJiYqFtfwKA7GbXdnkryZR3Jl3V6a75Sj1Vy55qf8fd04cPrJhHia7vitTM5Cwc+CQ3l4lc2c+eaIyz/0+R2LzLTm/TWPtZVJF/WkXxZx97zZYvhHzlAWKv7oUDe8doopRwBH6CEliPa/1RKZQJ/Be5VSt1kg5iEEKJHyq+o4+q3tuLq5MB//zDRpgW1LYT4uvHBHyfi4uTA1W9to6CizuiQhBDCLtiiqN4GxCilIpRSzsBiYFWbNquAJZbbi4D1usXpWutwrXU48C/gH1rrZTaISQghepzq+iaueXsbZbWNvHnVOJvOQW1LYf7uvHXVOEprGrjmnW1U1zcZHZIQQhiu00W11roJuAlYC+wHPtZa71NKPayUmmtp9gYtY6jTgFuB/5l2Twgh+rKmZjM3/XcnB45V8uKlYww7KbGjhoX48OKlY0jJq+DmD3bR1Gw2OiQhhDCUTS7+orVeA6xps+zBVrfrgAtP8hxLbRGLEEL0RE+tS+X71EIenT+MaXHBRofTIdPignl43jDuX5nM0+sOcvecOKNDEkIIw8gVFYUQwmBrko7yyg+HuWzCIC6fONjocKxy+cTBpByt4N8/pDMy1Ic5wwcYHZIQQhjCJldUFEIIcWoO5Vdyxyd7GD3IlwfPb3vdrJ7h7+fHMyrMl9s/2UNagVx1UQjRN0lRLYQQBqmsa+T693bg5uzAy5eNxcXRweiQTomLowMvXz4GN2cHrntvB5V1jUaHJIQQ3U6KaiGEMMgDK5PJLK5m2aVj6O/janQ4nTLAx41ll44hs6iaBz+XC+QKIfoeKaqFEMIAn+3MYeXuPP4yI5aJkQFGh2MTEyMDuGVGDCt25bJiV47R4QghRLeSoloIIbpZZlE1D6xMZny4PzdNjzY6HJu6aVo048L9uH9FMlnF1UaHI4QQ3UaKaiGE6EYNTWZu+XAXjg4mnls8CgeTMjokm3J0MPGvxaNxMClu+WAXDU0yf7UQom+QoloIIbrRC+sPsTennCcWDLe7S5DbSoivG08uHMGenHJeWH/I6HCEEKJbSFEthBDdZE92GS9tSGfhmNBeP5/znOEDWDAmhJc2pLMnu8zocIQQostJUS2EEN2grrGZ2z7ZQ7CXS4+dj9pafz8/gSBPF277ZA91jc1GhyOEEF1KimohhOgGz6xLJa2giicXjsDHzcnocLqFj5sTTy4aQVpBFc9+c9DocIQQoktJUS2EEF1sR1YJr2/K4LIJgzgjNsjocLrV1NggLp0wiNc2HmZHVonR4QghRJeRoloIIbpQfVMzd32axEAfN+49Z6jR4Rji3nOGMtDHjbs/TZLZQIQQvZYU1UII0YVe+eEwaQVVPDp/GB4ujkaHYwhPF0cenT+MQwVVvPJDutHhCCFEl5CiWgghukh6YRXL1qdx/siBTIsLNjocQ02LC+a8EQN4YX0a6YVVRocjhBA2J0W1EEJ0AbNZc89nSbg6mXjwvL4x28fJPHh+PK5OJu79LAmttdHhCCGETUlRLYQQXeCTHdlszSjhvnOHEuTlYnQ4diHYy5V7zxnKlowSPtmeY3Q4QghhU1JUCyGEjRVW1vPY6v1MiPDnosQwo8OxKxclhjE+wp/H1uynsLLe6HCEEMJmpKgWQggbe/jLFOoazfxjwXCUUkaHY1dMJsU/LhhObUMzj3yZYnQ4QghhM1JUCyGEDX1/oIAv9uRx0/RoooI8jQ7HLkUHe/LnaVGs2pPH96kFRocjhBA2IUW1EELYSHV9E/evTCYm2JMbpkYZHY5d+9OZUUQFeXD/imRqGpqMDkcIITpNimohhLCR5787RG5ZLY8vGI6zo7y9noiLowOPLxhBblkt//r2kNHhCCFEp8m7vhBC2MCh/Ere2JTBxYlhJIb7Gx1OjzA+wp+LEkN5c1MGB/MrjQ5HCCE6RYpqIYToJK01D36+D3dnB+6cPcTocHqUu2bH4eHiyP0rk2XuaiFEjyZFtRBCdNKXe4+y+XAxd8yOI8BT5qS2RoCnC3fNjmNrRgkrd+caHY4QQpwyKaqFEKITquqbeHR1CsNCvLl0/CCjw+mRFo8LY2SYL4+tPkB5baPR4QghxCmRoloIITrhhe8OkV9Rz8PzhuFgkjmpT4XJpHh03jCKq+t57puDRocjhBCnRIpqIYQ4RWkFLScnXpQYyphBfkaH06MND/Xh8gmDeXdzJsm55UaHI4QQVrNJUa2Umq2USlVKpSml7m5nvYtS6iPL+i1KqXDL8plKqR1KqSTLv9NtEY8QQnQ1rTV/X9VycuJds+OMDqdXuP3sIfi5O3P/ymTMZjlpUQjRs3S6qFZKOQAvAnOAeOASpVR8m2bXAqVa62jgOeBJy/Ii4Hyt9XBgCfBeZ+MRQojusDrpKD+lFXPHrCFycqKN+Lg7cc85Q9mdXcbH27ONDkcIIaxiiyPV44E0rfVhrXUD8CEwr02becA7ltvLgRlKKaW13qW1zrMs3we4KqXk00kIYdeq65t49Mv9JAz05tIJg40Op1dZOCaE8eH+PPn1AUqrG4wORwghOszRBs8RArQ+pJADTDheG611k1KqHAig5Uj1rxYCu7TW9e1tRCl1HXAdQEhICJmZmTYI3TrFxcXdvs2eTPJlHcmXdYzM1yu/HONYRR0PTB9A9pEsw+KwVk/pYzeM8+MPy0t4YPl2bp860LA4ekq+7IXkyzqSL+v0hHzZoqhu73T3toPhTthGKZVAy5CQs4+3Ea31q8CrAImJiTo8PNzqQG3BqO32VJIv60i+rGNEvtIKqvhkbwoXjg3l3IltR7rZv57Qx8LD4ZqjZt74KYNrpw1ltIEngfaEfNkTyZd1JF/Wsfd82WL4Rw4Q1up+KJB3vDZKKUfAByix3A8FVgBXaq3TbRCPEEJ0Ca01S389OXGOnJzYlf46M5ZgLxce+DyZZjlpUQjRA9iiqN4GxCilIpRSzsBiYFWbNqtoORERYBGwXmutlVK+wGrgHq31TzaIRQghusyapGNsSivi9llDCJSTE7uUp4sj958bT3JuBf/Z0nOG2Agh+q5OF9Va6ybgJmAtsB/4WGu9Tyn1sFJqrqXZG0CAUioNuBX4ddq9m4Bo4AGl1G7LX3BnYxJCCFurtlw5MX6AN5fJyYnd4rwRA5gSHchTa1MprGz3dBshhLAbNpmnWmu9Rmsdq7WO0lo/Zln2oNZ6leV2ndb6Qq11tNZ6vNb6sGX5o1prD631qFZ/BbaISQghbOmF9WkcLa/jkfkJcuXEbqKU4qF5CdQ1NvP4mv1GhyOEECckV1QUQoiTSCuo5PWNh1k0NpSxg/2NDqdPiQry5LozIvlsVy5bDtv/2f9CiL5LimohhDgBrTUPrGw5OfFuOTnREDdNiyHE140HPk+msdlsdDhCCNEuKaqFEOIEVu3JY/PhYu6YHScnJxrEzdmBv58fz8H8Kt7+KdPocIQQol1SVAshxHFU1jXy2Or9jAj14dLxg4wOp0+bGd+P6XHB/OvbgxwtrzU6HCGE+B9SVAshxHE8980hCqvqeWTeMDk50WBKKZaen0CTWfPol3LSohDC/khRLYQQ7dh/tIJ3NmdyyfhBjAzzNTocAQwKcOfGadGsTjrKjwcLjQ5HCCF+R4pqIYRow2zWPLAyGR83J+6cNcTocEQr150RSXiAO39ftY/6pmajwxFCiN9IUS2EEG18ujOH7Vml3D07Dl93Z6PDEa24Ojnw0LxhZBRV89qPh40ORwghfiNFtRBCtFJe08gTXx1gzCBfFo0NNToc0Y6psUHMGdafZd+nkV1SY3Q4QggBSFEthBC/89S6A5TWNPDI/GGY5OREu/XAefGYlOKhL1KMDkUIIQApqoUQ4jfbM0v4z5YjLJkcTsJAH6PDEScw0NeNv8yI4dv9+Xybkm90OEIIIUW1EEIA1Dc1c/dnSQz0ceP2s+XkxJ7gmikRxAR7svSLfdQ2yEmLQghjSVEthBDAi9+nk1ZQxaMXDMPDxdHocEQHODmYeHjeMHJKa3lpQ5rR4Qgh+jgpqoUQfV7qsUpe3pDG/FEDmTYk2OhwhBUmRQUwf9RAXvnhMBlF1UaHI4Tow6SoFkL0ac1mzV2f7sXL1YkHz08wOhxxCu49dygujiYeWJmM1trocIQQfZQU1UKIPu29zZnszi7jwfPi8feQOal7omAvV+6cPYRNaUV8siPH6HCEEH2UFNVCiD4rp7SGf65NZWpsEPNGDTQ6HNEJl00YzPhwfx79MoX8ijqjwxFC9EFSVAsh+iStNfevTAbgsQuGoZTMSd2TmUyKJxeNoL7JzH0rZBiIEKL7SVEthOiTVu3JY0NqIbefPYRQP3ejwxE2EBHowW1nx/Lt/ny+2HvU6HCEEH2MzBslRAc1NZvJLaslo6iaIyU1FFXWU1LTQGlNI41NZsy65einm7MD3m5OeLs60d/bhcEBHgwKcGeQvztODvI91h4UVNaxdNU+RoX5smRyuNHhCBu6dkokq5OO8ffPk5kY6U+wl6vRIQmgsdnMkZIajhTXkFVczbGKeirqGqmobaS2oRmlFCYFTo4m/Nyd8Hd3JtDLhUH+7kQEehDi64ajvH8KOydFtRDHkV1Sw+bDxezNKSMpp5z9RytpaDb/tl4p8HN3xtfNCWdHEyalUApqG5qpqGukvLaRxub/+wna1cnEsIE+jAzzZVy4H5OjA/F2dTJi1/o0rTX3fJpEdUMzT184Age5FHmv4mBSPHPhCM55fhP3fJrE60sSZWiPASrqGvk5rYhtmaXszi4jObec+qb/e/90clD4WA4+uDk7oDWYtaahyUxZbSOlNQ20HsHj7GBi6AAvhof6MCLUl0mRAYT5yy9Mwr5IUS2ERW1DMxsPFbL+QAE/pReRXVILgJeLI8NDfbj6tHCigj2JCPRgcIA7AR4uJyzItNYUVtVzpLiGzOIaUvIq2JtTxvu/ZPHGpgwcTYoxg/04a2gw54+Uk+S6y0fbsvnuQAEPnBdPdLCX0eGILhAd7MVds+N45MsUPt6ezcXjBhkdUp9QUNXIuh/T+XZ/ATuzSmkya1wcTQwP8eHyiYMZOsCb8AB3Bgd4EOjpfMIvO81mTXF1PVnFNWQUVZNeUMXenHI+35XH+78cASDM343TogKZHhfM6TFBuDk7dNeuCtEuKao76IXvDvHl7iM4O+eg0TiYTHi7OuLl6oiPmzMhvq6E+LkR5udOTD8vfNzkCGRPUNfYzDcp+azak8fGQ4XUNZrxcnVkUmQAf5gSyaSoAKKDPDGdwtFMpRTBXq4Ee7mSGO4PY1uWNzab2XWkjA2pBWxILeQfaw7w+FcHGNHfnUsnm5g7MkQ+HLrIkeIaHvkyhclRAVwtwz56tasnh/NtSj4Pf5HCpMhABgXIUc2uUNvQzKo9uXy2M5etGSVoIH6AN9edEcmZQ4IZPcj3lIa9OZj+7/1zXLj/b8vNZk1aYRWb04v5Ka2I1UlH+XBbNq5OJk6PCWLuyIHMjO+Hq5O8h/YE5bWNHMqvJLu0htzSWnLL6iivbaCyromKuiaazWYULb8CJw5w4cHwcKNDPiEpqjvI3cURX1dH3N1bvl03mTWVdY0cLa+jpLqBkuqG37Uf4ONKXH8vRg/yY8wgP0aG+eAlP/XbBbNZsz2rlM925rB671Eq65vo7+3K4nGDmBnfj/ER/l069tnJwcT4CH/GR/hz5+w4MouqWbUnj0+2ZXLXp0k8tno/FyaGccXEwYQHenRZHH1NU7OZ2z7ZjUkpnrpw5Cl9URI9h8mkePqikcx+7kdu+2Q3H143SYb62FBmUTXvbs5i+Y5sKuqaiAzy4OpxQVw5NaFL37dMJkVsPy9i+3mxZHI4jc1mtmaU8E1KPl8nH+OblHy8XBw5d8QAFowJZVy4nwz/sRNV9U3sPlLGziOl7DpSyoFjlRwt//30l/4ezvh7OFsOWDrhaFJordGAm5P9j6mXorqDrp0SwYxQRfhxviXVNjSTV15LVnE1qceqOJhfyb68cjYcLETrlm/dYwb5cuaQYM4cEkT8AG95oXez3LJaPtqWzYpdOWSX1OLu7MCcYQNYOCaEiZEBhhVZ4YEe3DIjhvMjHSnEh3c3Z/LOz5m89VMG5wwfwJ/PjCZ+oLchsfUmL6xPY1tmKc9dPJIQXzejwxHdIMTXjYfmJXDrx3t4Yf0h/npWrNEh9Xj78sp5aUM6XyUdxaQUc4YP4IqJgxkX7kdWVla3HwhwcjBxWnQgp0UH8sB58Ww5XMynO3NZtSePD7dlE+bvxoLRoVyYGCqz/HSzpmYzO4+UselQIRvTitiTXYZZt5yPFBPsycTIAGL7eTGkvyeDAzwY6ON2wl9pMzMzuy/4UyRFtY24OTsQFeRJVJAn0+P6/ba8oq6R3UfK2JpRwoaDBTy1NpWn1qYS7OXCmUOCfiuy3Z3lv6IraK3ZklHC2z9lsi7lGBqYEh3IrTNjmZXQ367yrpRifHjLEeyCijre+jmT9zZn8eXeo8yIC+a2s4dIcX2KNqcX88L6QywYE8IFo0ONDkd0owVjQtl0qIjnvzvExMgAJkYGGB1Sj7Qvr5xn1x3kuwMFeLk4cv3UKK6eHE6wt/3MruJgUkyODmRydCCPzE9g7b5jfLYzl+fXH+KF9YeYMbQfSyaFc1p0gBzU6iL1Tc38nFbc8qvB/nxKqhswKRgZ5sufz4xmXIQ/o8J8e+0QWfupKHopb1cnzogN4ozYIG6fNYSCyjp+SC1kw8FCvk4+xsfbc3BzcuCs+H7MHTmQqbFBODva/08c9q62oZnPd+fy9s+ZHDhWia+7E9edEcXlEwf1iKMVwd6u3DU7jhumRvHuz5m8tvEw5zy/kbkjB3LrzFgZFmKFkuoG/vrRLsIDPHhk3jCjwxEGeHj+MHZll/HXD3ez5i+ny+XorZBZVM2z3xxk1Z48fNycuG1mLFdODrf7osjd2ZELRodywehQcstq+e+WLD7cms03KflEBnlwxcTBLBwbKjMw2UBtQzPrDxTw9b5jfH+ggKr6JrxcHJk+NJhZCf05LTrQ7vuLrUhR3c2CvVy5MDGMCxPDaGo2sy2zlC/25vFV0lG+2JOHt6sjc4YNYO6ogUyMDJAxgFbKKa3hvV+y+GhbNmU1jcT19+LJhcOZNyqkR5644uPmxM0zYrhyUjiv/JjOmz9l8FXyUa6dEsnN06PxcJGX8ImYzZrbP9lDaXUjb141TvLVR3m6OPLCJaNZ8NLP3PHJHl67MlHG1J9EeW0jL3x3iHc2Z+JoMnHjtCiuOyOqRxZHIb5u3DErjltmxLAm6Sjvbs7ioS9SeGptKgvGhHDV5HCZCchKWmt2Hill+Y4cvtzTcm6Sv4cz540YwKxh/ZkcFYCLY8/7zO0sm3zCKKVmA/8PcABe11o/0Wa9C/AuLfMfFAMXa60zLevuAa4FmoFbtNZrbRFTT+DoYGJSVACTogJ4aG4Cmw4VsWpPHl/uzeOj7dn093Zl/ugQFo4JIaafvOCPp+0QD4BZCf25anI44yP8e8XPfD7uTtw5O46rJofzz7Wp/PuHdFbsyuHec4Yyd+TAXrGPXWHZ92msP1DAQ3MTSBjoY3Q4wkDDQny479yh/H3VPl78Po2bZ8QYHZJdMps1H27L5ul1qZTWNHBxYhi3zoy1q2Eep8rF0eG3o9dJOeW8szmTj7fn8P4vRzg9JpCrJoczbUiwfOE6gbyyWlbsymX5jhwyiqpxc3JgzvD+LBoTygQ5ENj5olop5QC8CMwEcoBtSqlVWuuUVs2uBUq11tFKqcXAk8DFSql4YDGQAAwEvlVKxWqtmzsbV0/j5GBiWlww0+KCqW1o5rsD+Xy2M5fXNh7m3z+kMyLUhwWjQ5g7KkR+urQ43hCPKyYN7rUnogV7u/L0hSO5ZPwg/r4qmb98uJv/bDnCw/MSiOsv461bW38gn+e+PcgFo0O4ctJgo8MRduDKSYPZdaSUZ789yLAQH6bFBRsdkl1JK6jk7k+T2J5VyvgIfx48L55hIb3zy+jwUB+evnAk98yJ48Nt2by3OYtr39nO4AB3rpwUzoWJMjTkV7UNzaxLOcbyHTlsSitCa5gQ4c+fz4xizvABeMovgL9RuvUli07lCZSaBCzVWs+y3L8HQGv9eKs2ay1tNiulHIFjQBBwd+u2rdudaJuJiYl6+/btnYr7VGRmZh539o+uUlhZz+e7W+YATTlagaNJMS0umIVjQpkeF2zX46+7Kl/tDfG4+rTwHjvE41fW5qvZrPloWzb/XHuAyromrpg4mNvOju0zUzeeKF8ZRdXMXbaJQf7uLL9hssz7bWHEe5i9qW1oZuHLP5NdWsMXN0054fkJfSVfDU1mXt6Qzovfp+Hu4sAD58azYEyI1b+A9eR8NTabWbvvGG//lMn2rFLcnR1YOCaUJZPDiQ727JJt2nO+2hveEeLrxqKxoSwcE2rIvO9G5UsptUNrndihtjYoqhcBs7XWf7DcvwKYoLW+qVWbZEubHMv9dGACsBT4RWv9vmX5G8BXWuvl7WznOuA6gJCQkLGbNm3qVNynori4mIAA484cTy+uY+3BMr45WE5pbRPeLg5Mj/ZhVqwPccFudjcEwJb5MmvNtuwqvkgp5eesSgCmRHizcJg/Iwa4292+n4pTzVdFXRNvbC1gVUopAR6O/HXKAKZE9P6j1sfLV3VDMzeuyKCktolXFkQywFt+2fmV0e9h9uJoRQPXf3qYAA9Hls2PwOM4X7r6Qr72HavhqR/yyCyt56xoH248rT9+bqd25LG35Cu1sJbPkkpYn1ZOo1kzLtSDBcMDmDDIE5MNP2vsMV8FVY2sO1jG16ll5JQ34OqomBrpw+whvowc6G7T/beWUfmKiIjocFFti2P27WW4baV+vDYdeWzLQq1fBV6FliPVRn27M/JbZXg4zBjbMvfjxrQiPt2Rw5qUfFbuKyEqyIMFY0K5YHQIA+1o6ENn81VQWccn23P4YOsRckprCfBw7tVDPE41X/8vLpqrs8u4+9O93L82m9kJ/XloXgL9esE4yBNpm6/GZjPXvL2N7PIG3rl6PJNiAo0JzI7Z65Gx7hQOvOTmz5K3tvLExiLevGrccS/41FvzVVXfxNNrU3lncyYDvF1566pxNhkO0xvyFR4Os8ZBUVU9H2w5wnu/ZHHPV0cID3DnsgmDmT86hCAvFxttK9wmz9MZVfVNfJPSMv1g6+Edf5kZanfDO+whXydii0zlAGGt7ocCecdpk2MZ/uEDlHTwsaINRwcT04YEM21IMOW1jXyVdJRPd+bw1NpUnl6XyuSoABaOCWX2MPuah7mjGpvN/JRWxEfbWqY/ajJrJkUGcNfsOM5O6NcnzyjuiFFhvnxx8xRe35jBv749yE/PFHHnnDguGz+oT5x4o7XmvhVJbDxUxD8XjmCKFNTiBKbEBPKPC4Zx16dJ3L8imScWDu8Vv3h1xPoD+dy/IpmjFXUsmRTO7bOG2FXhZC8CPV24eUYMN5wZxVfJx3jn50weW7OfJ78+wJlDglk01v6HYR5PfVMzG1ILWbUnj+/251PXaCbUz41bpscYNryjN7DFq2gbEKOUigByaTnx8NI2bVYBS4DNwCJgvdZaK6VWAf9VSj1Ly4mKMcBWG8TUZ/i4ObF4/CAWjx9EVnE1n+3M5bNdOdz68R7uX5n82/R8EyL87Xq8cbNZsyWjmC/3HuWrpKOU1jTi5+7ENVMiWDwujMigrhnT1ts4OZj405lRzBnWn/tWJvHAymRW7srliQXDe/0MMsvWp/Hx9hxunh7NRePCTv4A0eddPG4Q2SW1LPs+jTB/N26a3rtnBCmqquehL1L4Yk8esf08+fSyyYwZ5Gd0WHbPycHE3JEDmTtyIIfyK1m+M4cVO3P5dn8+fu5OzBsVwoIxIQwP8bHrL2Z1jc1syShh9d48vko+RmVdEwEezlyUGMbckQMZM8ivTxyA6UqdLqq11k1KqZuAtbRMqfem1nqfUuphYLvWehXwBvCeUiqNliPUiy2P3aeU+hhIAZqAG/vizB+2MjjAg7/NjOUvM2LYnlXKZztzWL235Si2m5MDp0UHMj0umOlxwfT3MX5YwK+XMF2TdJTVSUcprKzH3dmBs4b247wRA5g6JEiOSp+i8EAP3r92Ap/tzOWR1Smc8/xG/nRmNH8+m04+XwAAIABJREFUM8quv1ydqvd+yeKZb1pm+rh1plyKWnTcbWfHklNaw9PrDuLr7szlE3vfTDFaaz7dmcujq1OoqW/m1pmx3DA1qkceYTVaTD8v7pkzlDvOHsLGtCKW78jhv1uO8PbPmYT6uTE7oT9nJ/RnzCBfHI8zpKg7HSuvY/2BAtYfKOCntCJqG5vxcHZg1rD+zBsVwmlRAXYRZ29hk997tNZrgDVtlj3Y6nYdcOFxHvsY8Jgt4hAtTCbF+IiWy10vnZvAz+lFrD9QwPcHCvl2fz4A8QO8mTokiPHh/owZ7NctE/prrUkvrGJrRikbDxWyKa2IyromXBxNTI8L5rwRA5keFywzNdiIUoqFY0M5c0gQj67ez/PfHeLLvXk8fsFwJvSiSzV/tO0ID6xMZnpcME8uHGHXR4qE/VFK8c9FI6moa+L+lck4O5h61S8dR4pruHdFEpvSikgc7McTC4fLhU5s4HfDMGsaWZtyjK+Tj/Hu5ixe35SBl6sjU6IDOT0miPER/kQFeXTLe1N5bSM7s0rZmlnCD6mFpBytAPht5o7pccFMigrolQdX7EGnZ/8wQl+aUs+WtNYczK+yFNgF7DxSSpNZoxTEBnuRMNCb+IHexA/wJjzQg/7erqf8U1BDk5ktyYeocvBm/9EK9uVVsPNIKaU1jQAM8HFlamwQU2ODOD02SMbz0fX964eDhdy3Iomc0loWjwvjnjlD8XHvudPvZWZmsrPEkds+2cPpMUG8esVY+aA4iZ7+HtaV6hqb+eO729mUVsSzF43kgtGhPTpfTc1m3vwpg2e/OYijycRd3XB+RU/Ol61U1DWy6VARP6QW8sPBQo5V1AHg5+7E2MF+xA/wZugAb4b096K5ooCYqMhT2o7ZrDlWUUdmUTUpRytIyWv5nD1YUInW4GhSjBnkx/ShLb9OxwR79vgDDn1iSj0jSFFtGzUNTezOLmNbRim7sktJyaugoLL+t/UujiZC/dwI9nIl0MuFAA9nXJ0ccHUy4eLoQLPZTGOzpqHZTFlNI2U1DRRXN5BbWsvR8lrMlq5lUhAZ5MnoMF/GhfszNtyPyMDu+dbek3RH/6ppaOL/fXuI1zdl4OfuzNK58Zw7fECP/L9Y9tUunv0xj4mRAbx51TgpqDugt72H2VpdYzNXv7WNLRnF/OOC4UwMNvfIfCXllHPviiSScss5a2g/HpmfwACfrp8tSfrX72mtOVxUzY7MUrZllrAru4zDhVW/+2wc4ONGiJ8bAR7O+Lo74+vuhLODCScHhYPJRH1TM3WNZuoamymubqCosp6CyjpySmupbzL/tq1gLxfiB3ozOsyPcRF+jA7z63W/+kpR3UWkqO46hZX1HMyvJKOomqziarJLaimqqqewqp6S6gbqGptpbP59n3E0KXzdnfB1d8bf3ZkQPzfC/NxwM9dw2rAIYvt5ScHTAd3Zv5Jzy7nns5YP3RlxwTw8f1iPmaJQa80L69N49puDTI0N4uXLx/TIWW6M0BfewzqrpqGJG97fyY8HC7lmXDAPLEjsMV86y2sbeWZdKu/9kkWAhwsPz0tgzrD+3Ra/9K+Tq2ts5mB+JanHKknKOEql2Znc0lpKahooq2mgrKaRJvPvP2OdHBSuTg74ezgT5OlCoKcLYf5uDA7wICLQg9h+Xjab4s+e9YSiWj6JxO8EebkQ5OXCadHHn46s2axpaDLjYFI4mtRxf07MzMwkPNS3q0IVnTAsxIcVf57M2z9n8sy6g8x89gduP3sISyaH42DHZ383NZtZ+sU+3v/lCLNifVi2JPG48wsLcSrcnR15Y0kidy3fy5vbcmlwSGbp+Ql2fTKX1poVu3L5x5r9lFQ3sGRSOLeeHSuX2bZDrk4OjAj1ZUSoL+MCm9stEs1mTZNZ02zWODua7Po9WfyeFNXCag4m1et+VuqLHB1M/OH0SGYl9Of+lck8/GUKn+/O5fEFI4gfaH9XZCysrOeWD3ax+XAxN0yN4uI4FymoRZdwcjDxzEUjcdF1vP/LEdILqnn+ktF2eTQw9VglD3yezNaMEkaF+fL21eMZFuJjdFiiE0wmhbMU0j2SfCIJ0ceF+bvz9tXjeP6S0eSW1XL+sk0sXbWP4qr6kz+4m2zNKOHc5zeyK7uUpy8cyd1z4nrMT/KiZ1JKcf3E/jx94Uh2Hinl3Oc3si2zxOiwflNcVc/SVfs49/mNHMyv5PEFw/nsT5OloBbCQHKkWgiBUoq5IwdyRkwgT36dyrubM1m+I4cbpkZyzZQIw8Ys1zU2s2x9Gi//kM4gf3feuWY8QwfY31F00XstGhtKwkBv/vT+Dha/+gt/mhrFTdOjDTtPpKahiTc3ZfDvHw5T09DExeMGccesIfh7OBsSjxDi/0hRLYT4ja+7M48vGM61U8J58utUnl53kDd/yuTaKRFcMWlwt47R/Dm9iPtWJJNRVM2CMSEsnZsgY0SFIYYO8GbVzVNYumofy75PY3XSUf5xwXAmRXXffO8VdY28tzmLNzZlUFLdwNnx/bhzdhzRwXK1WSHshRTVQoj/ER3sxWtXJrIjq5Rl6w/x1NpU/v1DOpeOH8RlEwYzKMC9y7a9L6+c5787xNp9+Qzyd+f9aycwJeb4J84K0R28XZ149qJRXDA6hPtWJHPJa78wK6Eft8yIIWFg1w25yCqu5r9bjvDfrUeorGti2pAgbpoew9jBcnlxIeyNFNVCiOMaO9iPt64eT3JuOS9tSOP1TRm8uvEwZ8QEcVFiGNPigmwyNMRs1vySUczbP2WyLiUfL1dH/npWDNefESUnxQq7cnpMEGv/egav/JjOG5syWLsvn7Pj+3H1aRFMiPC3ycVVahqa+P5AIR9vz+aHg4U4mBSzEvrx5zOjZcy0EHZMimohxEkNC/HhpcvGcqy8jg+2HuHDbUe48b87cXUycWZsMNOHBpM42I8IKy7qU9/UTHJuOesPFLByVx65ZbW/FdNXnxaBj5sM9RD2yc3Zgb+eFcvVp0Xw5qYM3vwpg3Up+YT4ujF/9ECmxwUzLMQHF8eOfSHUWpNRVM32rFLW7y9gw8EC6hrN9PN24S8zYrhk/CD6+7h28V4JITpLimohRIf193HlbzNjuWVGDFszSvgq+ShfJx/j633HAAjwcCZ+oDdh/u6E+bkT4OmMo0nhYFLUNTZzrLyeYxV1pBdUsTunjIYmMyYFZ8QGcefsIZwd31+OTIsew8fNib/NjOWGqVGsSznGZztzeXlDOi9+n46zo4lRob5EBXvS39uV/j4uuDo50GyZg7i4qoHs0hqyS2pIyauguLoBaLky3kWJYcwZNoDxEf4yR7EQPYgU1UIIqzmYFJOiApgUFcDS8xNIL6xie1bLpXgP5VeRnHuU0prGdh8b6OlMmL87SyYNJjHcn8TBfgR42t/8v0J0lJuzA/NGhTBvVAjFVfVszyple2YJ27NK+SblGEVVDe0+zs/diTB/d6YOCWJcuD/jwv2IDPS0yRASIUT3k6JaCNEpJpMipp8XMf28uGT8oN+WV9Y1UlbTiFm3XBnMycFEsLdLh38SF6InCvB0YVZCf2Yl9P9tWX1TMwUV9TQ2t1yJ1qQUvu5OeMlsNkL0KlJUCyG6hJerFA1CALg4OhDm33Uz5ggh7INcUVEIIYQQQohOkqJaCCGEEEKITlJaa6NjsJpSqhDIMmDTgUCRAdvtqSRf1pF8WUfyZT3JmXUkX9aRfFlH8mUdo/I1WGsd1JGGPbKoNopSarvWOtHoOHoKyZd1JF/WkXxZT3JmHcmXdSRf1pF8Wacn5EuGfwghhBBCCNFJUlQLIYQQQgjRSVJUW+dVowPoYSRf1pF8WUfyZT3JmXUkX9aRfFlH8mUdu8+XjKkWQgghhBCik+RItRBCCCGEEJ0kRbUQQgghhBCdJEV1G0qpC5VS+5RSZqXUcaduUUrNVkqlKqXSlFJ3t1oeoZTaopQ6pJT6SCnl3D2RG0Mp5a+U+sayv98opfzaaTNNKbW71V+dUmq+Zd3bSqmMVutGdf9edJ+O5MvSrrlVTla1Wi7963/bjFJKbba8bvcqpS5uta5P9K/jvR+1Wu9i6S9plv4T3mrdPZblqUqpWd0Zt1E6kK9blVIplv70nVJqcKt17b42e7MO5OsqpVRhq7z8odW6JZbX7yGl1JLujdwYHcjXc61ydVApVdZqXV/sX28qpQqUUsnHWa+UUs9b8rlXKTWm1Tr76l9aa/lr9QcMBYYAG4DE47RxANKBSMAZ2APEW9Z9DCy23P438Cej96mL8/VP4G7L7buBJ0/S3h8oAdwt998GFhm9H/aWL6DqOMulf/1vm1ggxnJ7IHAU8LXc7/X960TvR63a/Bn4t+X2YuAjy+14S3sXIMLyPA5G75Md5Gtaq/eoP/2aL8v9dl+bvfWvg/m6CljWzmP9gcOWf/0st/2M3iej89Wm/c3Am63u96n+ZdnnM4AxQPJx1p8DfAUoYCKwxbLc7vqXHKluQ2u9X2udepJm44E0rfVhrXUD8CEwTymlgOnAcku7d4D5XRetXZhHy35Cx/Z3EfCV1rqmS6OyX9bm6zfSv9rfX631Qa31IcvtPKAA6NDVr3qJdt+P2rRpncflwAxLf5oHfKi1rtdaZwBplufrzU6aL631963eo34BQrs5RnvSkf51PLOAb7TWJVrrUuAbYHYXxWkvrM3XJcAH3RKZndJa/0jLwbbjmQe8q1v8AvgqpQZgh/1LiupTEwJkt7qfY1kWAJRprZvaLO/N+mmtjwJY/g0+SfvF/O8byGOWn3SeU0q5dEWQdqSj+XJVSm1XSv3y61AZpH+dtH8ppcbTcnQovdXi3t6/jvd+1G4bS/8pp6U/deSxvY21+3wtLUfJftXea7M362i+FlpeZ8uVUmFWPrY36fA+W4YVRQDrWy3ua/2rI46XU7vrX45GbtwoSqlvgf7trLpPa/15R56inWX6BMt7tBPly8rnGQAMB9a2WnwPcIyWQuhV4C7g4VOL1D7YKF+DtNZ5SqlIYL1SKgmoaKed9K//e54BwHvAEq212bK41/WvdnTkfadPvWedRIf3WSl1OZAITG21+H9em1rr9PYe30t0JF9fAB9oreuVUjfQ8qvI9A4+trexZp8XA8u11s2tlvW1/tURPeb9q08W1Vrrszr5FDlAWKv7oUAeUETLzxKOlqNBvy7v0U6UL6VUvlJqgNb6qKWoKTjBU10ErNBaN7Z67qOWm/VKqbeA220StIFskS/LMAa01oeVUhuA0cCnSP9qN19KKW9gNXC/5efBX5+71/Wvdhzv/ai9NjlKKUfAh5afWzvy2N6mQ/uslDqLli92U7XW9b8uP85rszcXPSfNl9a6uNXd14AnWz32zDaP3WDzCO2LNa+pxcCNrRf0wf7VEcfLqd31Lxn+cWq2ATGqZSYGZ1peGKt0y8j572kZNwywBOjIke+ebBUt+wkn39//GTtmKZR+HS88H2j37N9e5KT5Ukr5/TpMQSkVCJwGpEj/Om6+nIEVtIy5+6TNur7Qv9p9P2rTpnUeFwHrLf1pFbBYtcwOEgHEAFu7KW6jnDRfSqnRwCvAXK11Qavl7b42uy1yY3QkXwNa3Z0L7LfcXgucbcmbH3A2v/+lsjfqyOsRpdQQWk6u29xqWV/sXx2xCrjSMgvIRKDccsDE/vqXkWdJ2uMfcAEt337qgXxgrWX5QGBNq3bnAAdp+QZ5X6vlkbR8KKUBnwAuRu9TF+crAPgOOGT519+yPBF4vVW7cCAXMLV5/HogiZZi533A0+h9MjpfwGRLTvZY/r1W+tcJ83U50AjsbvU3qi/1r/bej2gZ5jLXctvV0l/SLP0nstVj77M8LhWYY/S+2Em+vrW8///an1ZZlh/3tdmb/zqQr8eBfZa8fA/EtXrsNZZ+lwZcbfS+2EO+LPeXAk+0eVxf7V8f0DJrUyMt9de1wA3ADZb1CnjRks8kWs3MZm/9Sy5TLoQQQgghRCfJ8A8hhBBCCCE6SYpqIYQQQgghOkmKaiGEEEIIITpJimohhBBCCCE6SYpqIYQQQgghOkmKaiGEEEIIITqpR15RMTAwUIeHh3f7dhsaGnB2du727fZUki/rSL6sI/mynuTMOpIv60i+rCP5so5R+dqxY0eR1jqoI217ZFEdHh7O9u3bu327mZmZGFHM91SSL+tIvqwj+bKe5Mw6ki/rSL6sI/myjlH5UkpldbStDP8QQgghhBCik6SoFkIIIYQQopN65PAPIYQQQojOqKhrJCmnnKTccvblVVBW00BDk5nGZjO+7s5EBXkQHezJqDA/Yvt5opQyOmRh56SoFkIIIUSfUN/UzPr9BXy2K5cNqQU0NmsAQnzd6OftgqODCTdnB/LKatmUVkRDkxmA6GBPzh0+gAVjQhgc4GHkLgg7JkW1EEIIIXq1usZm3v8li5c2pFNS3UCQlwtLJoUzdUgQwwb64Ofxv7NKNJs1OaU1/HiwkC/3HuX59YdY9n0ai8aEcvOMaEL93A3YE2HPpKgWQgghRK9kNms+2p7Nv749SH5FPafHBPKH0yM5LSoAR4cTn1bmYFIMDvDgikkeXDEpnGPldbz642He35LFZ7tyuHJSOLefPQQ3Z4du2hth76SoFkIIIUSvk1VczR2f7GVrZgljB/vxr4tHMykq4JSfr7+PKw+eH88fTo/g+e8O8camDDakFvCvi0czPNTHhpGLnkpm/xBCCCFEr6G15t3Nmcz+10b2H6vgqUUjWH7DpE4V1K0N9HXjiYUj+M8fJlBd38wFL/3Ei9+nobW2yfOLnkuOVAshhBCiV6hpaOKO5XtZvfcoU2ODeGLhcAb4uHXJtk6LDmTtX8/gvpVJPLU2lfSCKp5YOAJnRzle2VdJUS2EEEKIHi+7pIY/vrudg/mV3D0njuvPiOzyafB83J144ZLRDOnnxTPfHORoeR3/vnwsPu5OXbpdYZ9s8nVKKTVbKZWqlEpTSt3dznoXpdRHlvVblFLhbdYPUkpVKaVut0U8QgghhOg7dmSVMnfZJvLKannr6vHcMDWq2+aVVkpx84wYnrt4JNuzSlj0758pqqrvlm0L+9Lpolop5QC8CMwB4oFLlFLxbZpdC5RqraOB54An26x/Dviqs7EIIYQQom/58WAhl7++BR83J1bdNIWpsUGGxHHB6FDeuXo82aU1XP76FkqrGwyJQxjHFkeqxwNpWuvDWusG4ENgXps284B3LLeXAzOU5SukUmo+cBjYZ4NYhBBCCNFHrN57lGvf2UZEoAef3DCZ8EBjL8wyOTqQ168cx+Giaq58cyvltY2GxiO6ly2K6hAgu9X9HMuydttorZuAciBAKeUB3AU8ZIM4hBBCCNFHrNyVy00f7GRUmC8fXDeRIC8Xo0MCYEpMIK9cPpYDxyq4+q2t1DY0Gx2S6Ca2OFGxvUFLbeeVOV6bh4DntNZVJxv7pJS6DrgOICQkhMzMTOsj7aTi4uJu32ZPJvmyjuTLOpIv60nOrCP5sk535mtDejkPf5vDqAEePDKjP6X5uZR229ZPLsIVHpgRyt/XZfOnt3/mwZmhmNrUOdK/rNMT8mWLojoHCGt1PxTIO06bHKWUI+ADlAATgEVKqX8CvoBZKVWntV7WdiNa61eBVwESExN1eHi4DUK3nlHb7akkX9aRfFlH8mU9yZl1JF/W6Y58fZOSz6PfpTB2sB/vXDMed2f7nMgsPBzqHD34x5oDjDjUwK1nD2mnTXi3x9WT2Xu+bNETtwExSqkIIBdYDFzaps0qYAmwGVgErNcts6Sf/msDpdRSoKq9gloIIYQQ4qe0Im78z04SQnx486pxdltQ/+qPp0eSXlDN8+vTiAzyZP7otqNjRW/S6d6otW5SSt0ErAUcgDe11vuUUg8D27XWq4A3gPeUUmm0HKFe3NntCiGEEKLvSMmr4Pr3dhAR6MG7V4/Hy9X+54JWSvHI/GFklVRz56d7iQ72ZFiIXNK8t7LJVzyt9RpgTZtlD7a6XQdceJLnWGqLWIQQQgjRu+SU1nDVW1vxcnXk7WvG9aiLqzg7mnj5srGc8/xG/vyfnXx5yxS8e8AXAmE9uZamEEIIIexWWU0DV721jdrGZt65ZnyXXXa8K/l5OLPs0tHkltVy1/K9tIyAFb2NFNVCCCGEsEuNzWb+/J+dHCmu4bUrE4nt52V0SKds7GB/7pw1hK+Sj/Hu5iyjwxFdQIpqIYQQQtgdrTVLV+3j5/RiHl8wnImRAUaH1Gl/PD2SGXHBPLo6hUNFtUaHI2xMimohhBBC2J13N2fxny1HuH5qJAvHhhodjk2YTIqnLxyJr7sz/1ifS32TXBimN5GiWgghhBB2ZeOhQh76Yh9nDe3HnbPijA7Hpvw8nPnnwhFklNTz7DcHjQ5H2JAU1UIIIYSwG9klNdz8wS6igz351+JROJhOfMXlnmhaXDDnD/Xj1R8Psy2zxOhwhI1IUS2EEEIIu1Db0Mz17+3AbNa8ekUini72fXGXzvjT5H6E+blz68e7qa5vMjocYQNSVAshhBDCcFpr7vlsL/uPVfD/Fo8mPNDD6JC6lLuTA89cNJKc0lqeXpdqdDjCBqSoFkIIIYTh3vk5k5W787j1rFimxQUbHU63GBfuzxUTB/P2z5nsOlJqdDiik6SoFkIIIYShdh0p5bE1+zlraDA3Tos2OpxudcesIfTzcuXuT5NoaDIbHY7oBCmqhRBCCGGY0uoGbvzPTvp5u/LMhaMw9cITE0/Ey9WJR+YPIzW/kld+SDc6HNEJUlQLIYQQwhBms+bWj3dTVNXAS5eNwcfdyeiQDDEzvh/njhjAC+vTSC+sMjoccYqkqBZCCCGEIV7+IZ3vUwt54LyhjAj1NTocQy09PwEXRxNLV+1Da210OOIUSFEthBBCiG63Ob2YZ9alcv7IgVw+cbDR4RguyMuFv82MZeOhItal5BsdjjgFUlQLIYQQolsVVNZx8we7CA/04PEFw1Gqb42jPp4rJw1mSD8vHv4ihbpGuYR5TyNFtRBCCCG6TVOzmVs+2EVVfSMvXza2V1/gxVqODiYempdAblktL2+QkxZ7GimqhRBCCNFtnvv2IL8cLuGx+cMZ0t/L6HDszsTIAOaOHMjLP6RzpLjG6HCEFaSoFkIIIUS32JBawIvfp3NxYhgLx4YaHY7duvecoTiaFI+sTjE6FGEFKaqFEEII0eXyymr520e7ievvxUPzEowOx67193HllhkxfJOSz/epBUaHIzpIimohhBBCdKnGZjM3f7CLhiYzL102BlcnB6NDsnvXnBZBZKAHD63aR32TnLTYE9ikqFZKzVZKpSql0pRSd7ez3kUp9ZFl/RalVLhl+Uyl1A6lVJLl3+m2iEcIIYQQ9uPptansyCrl8YUjiAzyNDqcHsHZ0cTSuQlkFtfw+sYMo8MRHdDpolop5QC8CMwB4oFLlFLxbZpdC5RqraOB54AnLcuLgPO11sOBJcB7nY1HCCGEEPbju/35vPLjYS6bMIi5IwcaHU6PckZsELMS+rFsfRp5ZbVGhyNOwhZHqscDaVrrw1rrBuBDYF6bNvOAdyy3lwMzlFJKa71La51nWb4PcFVKudggJiGEEEIYLKe0hls/3kPCQG8eOK/t8TbREfefG49Za578+oDRoYiTsEVRHQJkt7qfY1nWbhutdRNQDgS0abMQ2KW1rrdBTEIIIYQwUEOTmRv/u4tms+bFS2Uc9akK83fnj6dH8vnuPHYeKTU6HHECtphxvb3LILW9aP0J2yilEmgZEnL2cTei1HXAdQAhISFkZmZaHWhnFRcXd/s2ezLJl3UkX9aRfFlPcmYdyZd12uZr2U9H2ZNdxtKZoVBVSGZVoUGR2Sdr+tc5kY78d4sj93+6ixfnR/TJK1D2hNejLYrqHCCs1f1QIO84bXKUUo6AD1ACoJQKBVYAV2qtj3v5IK31q8CrAImJiTo8PNwGoVvPqO32VJIv60i+rCP5sp7kzDqSL+v8mq+vk4+xPKmEqyaHc9UMmT7veKzpX3ef48ydy/eyt9yZeaPaDgjoG+z99WiL4R/bgBilVIRSyhlYDKxq02YVLSciAiwC1muttVLKF1gN3KO1/skGsQghhBDCQEeKa7hj+R5GhvpwzzlxRofTaywaE0rCQG+e/OoAtQ0yxZ496nRRbRkjfROwFtgPfKy13qeUelgpNdfS7A0gQCmVBtwK/Drt3k1ANPCAUmq35S+4szEJIYQQovvVNzVz4393ooBll47BxVHGUduKyaR48Lx48srreG3jYaPDEe2wxfAPtNZrgDVtlj3Y6nYdcGE7j3sUeNQWMQghhBDCWI9+uZ+k3HJeuWIsYf7uRofT60yIDGDOsP68vCGdi8eF0c/b1eiQRCtyRUUhhBBCdNpXB0p575cs/nh6BLMS+hsdTq91z5yhNJs1//w61ehQRBtSVAshhBCiU/Zkl/HsxqNMjgrgrtkyjrorDQpw55opEXy6M4eknHKjwxGtSFEthBBCiFNWVFXPDe/vwN/NkWWXjsHRQUqLrnbjtCgCPZ15+Mt9aN12FmNhFOn5QgghhDgljc1mbvzPTkqqG3hkVhj+Hs5Gh9QneLk6cdvZQ9iWWcqapGNGhyMspKgWQgghxCl5bPV+tmSU8MTC4cQGuRkdTp9yUWIYcf29ePyr/dQ1yhR79kCKaiGEEEJY7dMdObz9cybXnBbBBaNDjQ6nz3GwTLGXU1rLmz9lGB2OQIpqIYQQQlgpKaece1ckMTHSn3vlAi+GmRwdyMz4frz0fToFlXVGh9PnSVEthBBCiA4rqKjj+ve2E+jpwotyYqLh7j1nKPVNzTy77qDRofR58koQQgghRIfUNDRx7TvbKatt5JUrxhLg6WJ0SH1eRKAHSyaF89H2bPblyRR7RpKiWgghhBAnZTZr/vbRbpLzynl+8WiGhfgYHZKwuHlGDL5uTjzyZYpMsWcgKaqFEEIIcVJPfH0/F1ejAAAgAElEQVSAtfvyuf/ceM6K72d0OKIVHzcnbp0Zyy+HS1iXkm90OH2Wo9EBiFNXWt1AQWU95bWNVNQ24mBSeLs54u3qRH8fV7xcnYwOUQghRC/wxqYMXv3xMFdMHMw1p4UbHY5oxyXjB/Hu5iz+sWb//2/vzuOjrO7Fj3/OzGQmmez7vrKEfY0gCLgjLlfQasXagoha7d7ettfW3qs/u+l99Vrrr3axFde6a5VeLYgoBRRkk31JQkhICEnIvieznPvHPMQRA8mQZSbJ9/16zWueeeZ5Zs7zzZnJd85zznm4JDcem8Xs7yKNOJJUDyHl9W28u+8kO0vq2FvWwIn6tnNunxoVwtjEMCanRTFvdBzTM6IIkgElQgghfPD27hP8/H8PctXERB68fiJKKX8XSXTDYjbxn9dNYNmqbTz3cQl3Lcjxd5FGHEmqA1yn081bu0/wxs4ythXXojVkxtqZnhHFsjmZpEXbiQwJIjzYgltrGtudNLQ5KKtrJb+iicMVTfwrv4DH1xcQajVz0eg4/m1qCleMTyTEKr9ihRBCnN3G/FP88LU9zMqO4XdLp2M2SUIdyBaMjefS3HgeX1/AjTNSZSDpIJOkOkA5XW7+/ukJfre+gLK6NnLiQ/n+FWNZPC2FzNhQn16rodXBlqJqNhVUs+5gJe8drMRuNbNoYhK3XZjJjIwoaXkQQgjxOTtLarnnhZ2Mig/jL8vyCA6Shpih4P5rJ3DVYxv5n3X5/OqGyf4uTr/42Vv7SLI5+VZWlr+Lck6SVAegT4/X8aPX91JY1cyk1Ah+vmQSl4yNP+/EN9IexKJJySyalMxDiyfxybEa/rGnnH/sOcmbn55gfHIEy+dkcsOMVOmDJYQQgj2l9dy+ajuJEcE8d8csIkNkjM5QMTohjNvnZrHqo2MsvSCdKWlR/i5SnxRXt/C3T46zbEa8v4vSI+lgG0AcLjePvneEm/60hdYOJ3+8bQb/+NY8Ls1N6LeWZLNJMXdUHL++cQqf/PRyfnnDJLTW3PfmPhb894f8dVMRrZ3OfnkvIYQQQ8+B8gaWrdpGVGgQL941m4SIYH8XSfjoe1eMIS7Mxn++fQC3e2hPsffslmIsJsX1E6P9XZQeSVIdIE42tPGlP37M4x8UsnhaCmu+v4CrJycPaLeMUJuF22Zn8s/vzuf5lbPIig3lF+8cYt4jH/L7DwpoaHMM2HsLIYQIPPtPNPC1p7YRZrPw4p0XkhwZ4u8iifMQHhzET68Zx57Sel7dUerv4py3pnYHr+0o47opKcTaA/9siXT/CACHTjay4untNHc4+cNtM7hmcvKgvr9Sivlj4pk/Jp4dxbU88WEhv3kvnz//q4hlczO5a34OUXbroJZJeHQ4XZTVtVFe38appg6qmjqobemkqd1Jc4eTtk4nTrfG5dZoDRazwmo2YQsyE20PItpuJSbUSnSoldhQz3JadIhMtyiE+IIdxbWseGY7EcGeFur0GLu/iyT6YMm0VF76pJRH1hxm0aSkIfl//I2dZTR3OLl9bha46v1dnB5JUu1nHxVWc8/zOwm1WXjtnjmMT47wa3nysmJ4esUsDpQ38IcPj/KHDUd57uMSVs7PZuW8bEnGBojLrTle38HePeUcKG/gYHkjhVXNVDS2c+bFsWwWE+HBnhlfQoLMBJkVJpNCAU63ptPppt3hor7NQX1r92cb4sKsZMaGkhlrJ8u4z00KZ1R8mEy7KMQItKngFHc/t5PkyGBeuHM2KVHSQj3UKaV4aMlErn18M4+sOcKvbxxagxbdbs2zW0qYkRHF1PQoioslqRbnsP5QJfe8sJOcuDCeueOCgDrNNjElkidum8GRiiYeXXeEx94v4JmPi/n6glEsn5uJ3SpVpy8a2hxsO1bLlqM17C6t43BFE62dLgCCzIoxCeHMyYklI9ZORoydtGg7CeE24sNthNp6H3uny01Dm4Palk5qWzqpbu7keG0rJTUtFNe0sOVoDW/uOtG1vdViIjcxnAnJEUxI8dwmpkTI33uY0FrT0uGkrrWT+lYHda2d1LU6qG/tpLHNQUuni9YOp+e+00lLh4s2hwuny43TrXG4dNeyy60xKTApz4+608tmkyIkyEyI1YzdajaWLYRazUTZg7rOmnifRYmxWzHJVG1+8/buE/zotb3kxIfy/MrZxIfLNGzDxbikCFbMzeKvm49x44xULsiK8XeRem1DfhXHqlv4/q3T/V2UXuuX/5RKqUXA7wAz8Fet9cNnPG8DngNmAjXALVrrYuO5nwArARfwHa312v4oU6DbWlTDN/62i/HJEbxw52wiArQFODcpnD9/LY99ZQ08uu4Ij6w5zFObi/jGJaP5yuwMmWKpl1o7nV1J9JaiGvafaMCtPa3OU9Oi+HJeOonWThZMyWFMQjhWS/+0FlvMJmLDbOecq7Td4aK4poUjFU0cLG/kQHkj6w5V8orRD89sUoxLCmd6RhQzMqKZnhFNVqxdpmEMIC63prq5g4qGdioa26lsbP/cck2z50dVXUsnDvfBs76O1WzCbjNjDzJjt3kSYVuQGbvVgsWssJhMBJkVFrMJswJtvLfWnnu39iTbbQ4XTe1Oqho7aHU4aet0dSXo3QkyK5IjQ0iJCiY1yk5qVDApUSFkxNoZnRBGfJhN6tsA0Frz+w8K+Z91+czKjuHJr80ckl0ExLn9YOFY/rm/gp+8uY93vjNvyMzy9fRHxSRG2Lh6UpK/i9JrfU6qlVJm4AngSqAM2K6UWq219v7mXgnUaa1HK6WWAo8AtyilJgBLgYlACvC+Umqs1rr7b95hYm9ZPXc+u4OMGDvPrJgVsAm1t8lpkTy9YhY7S2r5zdp8Hvrfgzy5sYhvXz6am2em91sSOJzUt3by/qEq1uyvYGPBKTqdboLMiunp0Xz7sjHMGRXL9Iyori+44uJislIiB72cwUFmxiVFMC4pgsXTUgHPP9vKxg4OlDewp7SeXcfreevTcl7YehyAmFAr09OjuhLtKelRhPnQgi58o7WmrtVBSU0LJTWtFBv3JTUtlNe3c6q5A9cZI/wtJkVCuI2EiGDSY+xMSYvE5GgjKyWeaHsQUfbTrcWe5YjgoAH/HLc7XNS3es6c1LV6Ev2a5g4qGjsor/eMHfj4aDWVje14H054sIVR8WGMTghjVHwYuUlhTEqNJCFcZqU4Xx1OFz99cz9v7CrjhumpPPylyUMm2RK+sVst/OKGSax4ejt/3HCU710x1t9F6tHesno2FVTzo6tyh1SXxP74LzgLKNRaFwEopV4GFgPeSfVi4EFj+XXg98rT7LAYeFlr3QEcU0oVGq+3pR/KFZCKq1tYvmobUfYgnl85m5jQodUqMDMzhpfuvpCPC6v5zXtHuP/v+/nTv47y3cvHsmRaCpYhVPkHQlVjO2sPVrJ2fwVbimpwuTUpkcHcNjuDy8YlkJcZMySuZKmUIikymKTIYC4fnwh4WiILq5r59Hgdu47Xset4PesPVwFgUpCbFMEMI8memRlNprRm+0RrzammDoq7kubTibPncVP7Z1NdKgUpkSFkxNiZNyaOpIhgEiODSYoINpZtxIbavnD1u+LiYrL8ePGE4CAzSZFmkiLPnQw7XG4qGtoprmnhaFUzhaeaOVrVwr/yT/H6zrKu7RIjbExKiWRSquc2NV0S7d4orW3lmy/uYm9ZA9+7YgzfvXyMfFaHuUtzE7h+agp/+PAo101JZnRCuL+LdE6PvV9AlD2IZXMy/V0Unyh95igoX19AqZuARVrrO43HXwNma62/5bXNfmObMuPxUWA2nkR7q9b6BWP9U8A/tdavd/M+dwN3A6Smps7cvHlzn8p9PmpqaoiNjT3v/dscbr7x9yJqWp384YZs0iKHdr81rTXbSpt5alsV+dXtpEdZuT0vgUtyIjCbVJ/jNVSUN3ay6Vgjm4oaOVDZhgbSI60syIlgfnYEufHBvfqHNRTj1dTh4lBVGwcqWjlY2crBqjZaOt0ARAabmZhoZ2JiCBOT7OTGhxAS1H8/uoZivFxuzakWBycaOilv7OREQycnjPvyxk7anZ99H5sUJIdbSYm0khphJTXSuEVYSQoPwnYercpDMWZnaupwUVTTTn51O/mn2iiobud4fUdXy3ZKRBCTkuxMTrIzKclOZrQN03kmjMMhXmfaWtLELz84gVtr7rs0lfnZ/Tc4fjjGayANdrzq2pwse7mQzCgrv1ucHbCXnD9U2cq9fz/GXbMSuM3rgi/+ql/Z2dk7tdZ5vdm2P1qqu/urnJmpn22b3uzrWan1k8CTAHl5edpfrS3n+75aa77z8m5K6jp49o5ZzBsT+FcG6o3sbPjyfM3aA5U8uu4IP3+/jOdj7dw5P4cL4qL92io2ULTWFFQ1s2Z/BWv2V3DwZCMAE1Mi+MGV6SyalMTohLDzavkZivGanPvZ8unW7F3H69hZ4mnR/njbZ63Zo+LDmGy0Kk5Oi2RCcoRPAy/PFIjxcrjclNW1ddtVo7S2jU6Xu2tbq8VERoydnMRILp0QSlasnYxYz31KVMiAnPYMxJj56sw5DFo7nRwsb2R3aT07iuvYUVLLe/kNAESGBJGXGc1Fo+O4aHQcYxN9+2wOh3gBtHW6+O+1h3n6o+OMSwrnT1+dSVZcaL+/z3CJ12AZzHhlAT9fEsL3XtnNulI391w8atDe2xcPfriNaHsQ3712+he6FQZ6/eqPpLoMSPd6nAaUn2WbMqWUBYgEanu577Dw1OZj/GNPOT9elMv8YZJQn6aUYtGkJK6ckMia/RU8ufEoP3trP5HBZlbMc7JsTtaQ6+ZyJq01e8saWHOggrX7KyiqbkEpmJkRzc+uHc9VE5NkTlc8gxpzk8LJTQrn1lkZANS1dPJpaR27SxvYf6KBTYXVvPmpZ8YRpSA7LpSxCeGMSfT0mT3dbzZQB8Ge7qZRWtdKaW0bpbWtny3XtXKyof1z/ZvtVjOZsaGMTQznyglJZMbau6YyTIoIllkv+oHdaiEvK4a8rBjunO/5G5XUtLK9uJadJXVsKarp6qoUH27jolGxXUn2SJg6bmdJHT98bQ/HqltYNieTn1w9fkh0QxP9b/G0FNYeqODR9/K5eGy836fxPdOu43VsOHKKHy/KHZLjdPqjxNuBMUqpbOAEnoGHXzljm9XAcjx9pW8CPtBaa6XUauBFpdSjeAYqjgG29UOZAsrOklp+/c/DXDUxkXsD9JdhfzCbFNdOSeaayUl8cqyWx9bs57H3C/jTv45y88x0ls3JZExiYPfj8uZ0udleXMfaAxWsPVDByYZ2LCbFnFGx3DEvm4UTEuXyvb0QHWrlsnGJXDYusWtdVWM7+040sO+EZ07u/Kom1h2q7EpGlYK06BDSouykRoeQEhVCqjEzRHJUMDF26xcG5vWV261panfS0OaguqWDqsZ2qpo6qGxsp7LRc3+yoZ3S2lY6nO7P7RsfbiM9OoSZmdFkxNjJNFqbM2NDiQuzSn/VQaaUIisulKy4UG7O87TblNW18nFhDZsLq9lUUM1buz3tNznxoVw0ypNgzxkVS2RI4A8c7626lk4eXZfP3z4pITkyhBfvnM3c0XH+LpbwI6UUv1gyie3Fm/jBq3t4+5sXBdREA4+9X0BMqJXlc7L8XZTz0uekWmvtVEp9C1iLZ0q9VVrrA0qph4AdWuvVwFPA88ZAxFo8iTfGdq/iGdToBL453Gb+aO108oNX95ASFcxvbp46Iv65KqW4MCeWh6/JxBESy182FfHK9lKe31rCzMxoll6QzjWTk/t02n+g1Ld28q/8U6w/VMWGI1U0tjuxWUwsGBvPDxfmcvn4BJlyqh8kRARzecRngyDBMxtBcXUrhVXNFFQ1cfRUC+X1bWwuqKay6YsXwQGICM4nym4lyh5EZIinn7HFZMJiVgSZP5v+zeXSdLrcdDrdn9073TR3eJLohjYHje2Obt/DbFLEh9lIjLAxKj6US8bGkx7jmT88PSaEtGh7wLaqi8+kRdv58gV2vnxBOm635khlEx8VVvNRYTVv7Crj+a0lmBRMTY8yrjAbR7Srf3+4DRaHy81L247zP+/l09zhOVv47wvHysW7BACxYTYevnEydz63g9++n89/LBrn7yIBsOFIFRvzT/HTa8YFZH7QG30eqOgPeXl5eseOHYP+vuczcv6/3t7P81tLePmuC5mdM7IGcHjHq7q5gzd3lfHy9lKKTrUQHGTisnEJXDclhUty4/12cRGny83Bk41sOeo5PbyzpA6XWxMbauXScQlcPi6BBWPjB+UD7u+ZGQLZ6dkgTtS3cbKhjboWByUnT6FsodS3dnZdPbLT6cbpduN0aRyn711uzCaF1WLCajYRZDZhs3juw4ItRIYEfeEWG2YlITyYxIhgYkKtATugx1dSx7rX6XTz6fG6rlbsvWX1uDXYg0zMHe1JsOeNiSMnLjSgG0Y6nW7e3FXGExsKKa1tY+6oWB74t4nkJg3OGUKpX77xd7z+4/W9vLqzlGdWzOLisf7tltrucHHVYxsxmxRrvrug29Zzf8VLKTWoAxXFWXxUWM1zW0pYOS97xCXUZ4oLs3H3glHcNT+HnSV1rN5Tzrv7TvLuvgqsZhOzc2K4eGw8c0fFkZsUPmBJTLvDxZ7SerYX1/LJsVp2ldTRYlzJcHxyBPdePIrLxycwNS1K+roGkCCzifQY++f6rRcXK/kHLvqF1WJidk4ss3Ni+feFuTS0Ovj4aDXvfnqM3RWNvH+oEoDUqBDmjfYk2BeNjguYsSLVzR28sbOM57aUcKK+jalpkTxw3UQuH58Q0D8ChH89eP1E9pTV872XP+Wd78z36/iCJzcWUVLTygsrZwdUdxRfSVI9QBrbHfz4dc9lX390VW7PO4wQSqmuAUX/dd0Eth2r5YPDVWzIP8Uv3jkEQKjVzPSMaCamRnQNYMuMCSUixNLrfxBtnS7K6jwDyIpOtXC4oonDFY3kVzR3zb6QmxjOjTPSuCA7hllZMT3OnSuEGBki7UFcPTmZ8eEdZGVlUVLTwqaCajYXVPPu/pO8sqMUpWBMQhgzM2OYmRlN3iDPzd7ucBl9w0/w3oEKHC7NrOwYfnnDJC4eGy/JtOhRiNXME7fN4Pr/v5lvvriLV+6e45eEtrS2lSc+LOTaKcnMGzO0+/xLUj1AHn0vn5MNbbxx71zpb3kWFrOJuaPjmDs6jp/hGUi0o9gzFdvOkjpWbT6Gw6tPo81iIjEimGh7EMFBZkKsZiwmhcM4xd/a6aLeuEpbo9eFMsAzkGxcUjgrLsoiLyuGC7KipW+0EKJXMmNDyYwN5asXZuJ0udl7ooGPCqrZUVLH/+4t56VtniuNxoVZPVcYTYtkQkoE45MjSIro3Tz1PXG5NUcqmthZUsvmwmo25lfT5nAZF8jI4tZZ6QF/QQ8ReEbFh/HITVP41ouf8qt3D/Hg9RMH9f211jy4+gAWk+I/r50wqO89ECSpHgAHyxt5bksxX70wk+kZ0f4uzpCRFm0nLdrOkumeS2U7XW5KalspqGyirK6tayaGhjYHbZ0uals6cbo0QcagtPBgCxkxdmJCrcSFWbu6C2TG2IkNG9oX2hFCBAaL2cSMjGhmGN/tbrdn3vodJZ7p+3aV1PHewcqu7cNsFrKNmUjSokNIDLeRGBFMlN1KqM1MqM2CxaRwuTVu7TnLVtvaSV1LJycb2ik61cyxas/ZtuYOT2NBcmQwN+elsXBCErNzYobUZZxF4LluSgo7S+p4+qNicuJDWTaIM2+8vL2U9Yer+Nm144fF2WJJqvuZ1poHVu8nym7lB1eO9XdxhjSL2cSoeM+cxUIIEYhMXnOz3zbbc0nlpnYHhyuaOHSykaNVzRyraWV3aR1r9p/83Nm33ogPt5ETF8oN01OZmRnNzMxo0qJDpHuH6Ff3XzOe0tpWHlx9gOTIEK6ckNjzTn10oLyBB1YfYP6YOO64KHvA328wSFLdz97eXc724joevnGydC8QQogRKDw4iAuyYrggK+Zz691uTV1rJxXGGbfWDhctnU6cLo3ZpFAKQoLMxIRaiQ61khBuk2nwxKCwmE08fut0bn1yK99+aRcv3z2HaelRA/Z+Te0Ovvm3XUTbg3jslmnDZmIASar7UVO7g1++e4ipaZF8OS+95x2EEEKMGCaTIjbMJt3RRECyWy08dfsF3PCHj1jx9Daeu2M2k9Mi+/19tNbc98Y+SuvaeOmuC4fV50E6YvWjP244yqmmDv7f4knD5leXEEIIIUaGuDAbL6ycTajNwq1/2conRTX9+vqnBya+s+8kP1yYy6zsmJ53GkIkqe4nVY3trProGIunpQzoKRMhhBBCiIGSGRvKa/fMITHCxrJV2/jwcFW/vO7phPrZLSXcvSCHey7O6ZfXDSSSVPeTxz8owOnSMjhRCCGEEENacmQIr359DqMTwlj57HZ+uy4fp3GNh/PhcmseMBLqry/I4SdXjxuWg20lqe4HJTUtvLytlKWz0smMDfV3cYQQQggh+iQ2zMYrX5/Dkmmp/G59AUuf3EpZXavPr1Nc3cItf97Cc0ZCfd8wTahBkup+8ei6fCxmxXcuG+PvogghhBBC9Iswm4VHb5nGY7dM43BFEwt/u5FfvXuIqsb2HvftcLp45qNjXP27TeRXNvHbW6YO64QaZPaPPjtY3sjbu8v5xiWjSIgY+hOXCyGEEEJ4WzI9lRkZ0Ty67gh/3VTEMx8Xs2RaCnNHxTE1PYqsWDtOt6ahzUFJTQtvfVrOP/aWU9/q4OKx8TzypSnD4uIuPZGkuo8eX19AeLCFry8Y5e+iCCGEEEIMiIxYO48tnc73rxzLnzcW8danJ3h1RxkAVrOJTq8+1zaLiYUTk/jSjFQuHhs/rFunvUlS3QcFlU2sOVDBty8bTaRdJugXQgghxPCWGRvKr26YzEPXT6Sgqpk9pfUUVbcQZrMQZQ8iLszGvDFxRIzACxdJUt0Hf9xwlJAgMyuGyeU1hRBCCCF6w2I2MT45gvHJEf4uSsCQgYrn6XhNK2/vKecrszOICZXLkQshhBBCjGSSVJ+nP288ilkp7po//CYvF0IIIYQQvpGk+jxUNrbz2o4yvjQzbUSMZhVCCCGEEOcmSfV5WLX5GE63m3svlhk/hBBCCCFEH5NqpVSMUmqdUqrAuI8+y3bLjW0KlFLLjXV2pdQ7SqnDSqkDSqmH+1KWwdLS4eSlbce5elIyGbF2fxdHCCGEEEIEgL62VN8HrNdajwHWG48/RykVAzwAzAZmAQ94Jd+/0VqPA6YDFymlru5jeQbcm7vKaGx3cse8LH8XRQghhBBCBIi+JtWLgWeN5WeBJd1scxWwTmtdq7WuA9YBi7TWrVrrDwG01p3ALiCtj+UZUG6tefrjYqamRTIjo9tGeSGEEEIIMQL1NalO1FqfBDDuE7rZJhUo9XpcZqzropSKAv4NT2t3wNpe2kzRqRbumJc9Yq4OJIQQQgghetbjxV+UUu8DSd08dX8v36O77FN7vb4FeAl4XGtddI5y3A3cDZCamkpxcXEv377/vLizgli7hQnhHX55/6GmpqbG30UYUiRevpF4+U5i5huJl28kXr6RePlmKMSrx6Raa33F2Z5TSlUqpZK11ieVUslAVTeblQGXeD1OAzZ4PX4SKNBaP9ZDOZ40tiUvL09nZWX1VPR+VVDZxJ7KA/xw4VjGjJK5qXtrsP9OQ53EyzcSL99JzHwj8fKNxMs3Ei/fBHq8+tr9YzWw3FheDrzdzTZrgYVKqWhjgOJCYx1KqV8AkcD3+liOAff0x8UEmRW3zsrwd1GEEEIIIUSA6bGlugcPA68qpVYCx4GbAZRSecA9Wus7tda1SqmfA9uNfR4y1qXh6UJyGNhl9FH+vdb6r30s04BYPDWFhCAHsWE2fxdFCCGEEEIEmD4l1VrrGuDybtbvAO70erwKWHXGNmV03986IM3OiSXR1OTvYgghhBBCiAAkV1QUQgghhBCijySpFkIIIYQQoo8kqRZCCCGEEKKPlNa6560CjFLqFFDih7eOA6r98L5DlcTLNxIv30i8fCcx843EyzcSL99IvHzjr3hlaq3je7PhkEyq/UUptUNrnefvcgwVEi/fSLx8I/HyncTMNxIv30i8fCPx8s1QiJd0/xBCCCGEEKKPJKkWQgghhBCijySp9s2T/i7AECPx8o3EyzcSL99JzHwj8fKNxMs3Ei/fBHy8pE+1EEIIIYQQfSQt1UIIIYQQQvSRJNVnUErdrJQ6oJRyK6XOOspUKbVIKXVEKVWolLrPa322UuoTpVSBUuoVpZR1cEruH0qpGKXUOuN41ymlorvZ5lKl1G6vW7tSaonx3DNKqWNez00b/KMYPL2Jl7Gdyysmq73WS/364jbTlFJbjM/tXqXULV7PjYj6dbbvI6/nbUZ9KTTqT5bXcz8x1h9RSl01mOX2l17E6wdKqYNGfVqvlMr0eq7bz+Zw1ot43a6UOuUVlzu9nltufH4LlFLLB7fk/tGLeP3WK1b5Sql6r+dGYv1apZSqUkrtP8vzSin1uBHPvUqpGV7PBVb90lrLzesGjAdygQ1A3lm2MQNHgRzACuwBJhjPvQosNZb/BNzr72Ma4Hj9N3CfsXwf8EgP28cAtYDdePwMcJO/jyPQ4gU0n2W91K8vbjMWGGMspwAngSjj8bCvX+f6PvLa5hvAn4zlpcArxvIEY3sbkG28jtnfxxQA8brU6zvq3tPxMh53+9kcrrdexut24Pfd7BsDFBn30cZytL+Pyd/xOmP7bwOrvB6PqPplHPMCYAaw/yzPXwP8E1DAhcAnxvqAq1/SUn0GrfUhrfWRHjabBRRqrYu01p3Ay8BipZQCLgNeN7Z7FlgycKUNCIvxHCf07nhvAv6ptW4d0FIFLl/j1UXqV/fHq7XO11oXGMvlQBXQq4n6h4luv4/O2MY7jq8Dlxv1aTHwsta6Q2t9DCg0Xm846zFeWonefIIAAAQ6SURBVOsPvb6jtgJpg1zGQNKb+nU2VwHrtNa1Wus6YB2waIDKGSh8jdetwEuDUrIApbXeiKex7WwWA89pj61AlFIqmQCsX5JUn59UoNTrcZmxLhao11o7z1g/nCVqrU8CGPcJPWy/lC9+gfzSOKXzW6WUbSAKGUB6G69gpdQOpdTW011lkPrVY/1SSs3C0zp01Gv1cK9fZ/s+6nYbo/404KlPvdl3uPH1mFfiaSU7rbvP5nDW23h9yficva6USvdx3+Gk18dsdCvKBj7wWj3S6ldvnC2mAVe/LP58c39RSr0PJHXz1P1a67d78xLdrNPnWD+knStePr5OMjAZWOu1+idABZ5E6EngP4CHzq+kgaGf4pWhtS5XSuUAHyil9gGN3Wwn9euz10kGngeWa63dxuphV7+60ZvvnRH1ndWDXh+zUuqrQB5wsdfqL3w2tdZHu9t/mOhNvP4BvKS17lBK3YPnrMhlvdx3uPHlmJcCr2utXV7rRlr96o0h8/01IpNqrfUVfXyJMiDd63EaUI7nmvRRSimL0Rp0ev2Qdq54KaUqlVLJWuuTRlJTdY6X+jLwd621w+u1TxqLHUqpp4Ef9kuh/ag/4mV0Y0BrXaSU2gBMB95A6le38VJKRQDvAD8zTg+efu1hV7+6cbbvo+62KVNKWYBIPKdbe7PvcNOrY1ZKXYHnh93FWuuO0+vP8tkczklPj/HSWtd4PfwL8IjXvpecse+Gfi9hYPHlM7UU+Kb3ihFYv3rjbDENuPol3T/Oz3ZgjPLMxGDF88FYrT095z/E028YYDnQm5bvoWw1nuOEno/3C33HjETpdH/hJUC3o3+HkR7jpZSKPt1NQSkVB1wEHJT6ddZ4WYG/4+lz99oZz42E+tXt99EZ23jH8SbgA6M+rQaWKs/sINnAGGDbIJXbX3qMl1JqOvBn4HqtdZXX+m4/m4NWcv/oTbySvR5eDxwyltcCC424RQML+fyZyuGoN59HlFK5eAbXbfFaNxLrV2+sBpYZs4BcCDQYDSaBV7/8OUoyEG/ADXh+/XQAlcBaY30K8K7XdtcA+Xh+Qd7vtT4Hzz+lQuA1wObvYxrgeMUC64EC4z7GWJ8H/NVruyzgBGA6Y/8PgH14kp0XgDB/H5O/4wXMNWKyx7hfKfXrnPH6KuAAdnvdpo2k+tXd9xGebi7XG8vBRn0pNOpPjte+9xv7HQGu9vexBEi83je+/0/Xp9XG+rN+NofzrRfx+jVwwIjLh8A4r33vMOpdIbDC38cSCPEyHj8IPHzGfiO1fr2EZ9YmB578ayVwD3CP8bwCnjDiuQ+vmdkCrX7JFRWFEEIIIYToI+n+IYQQQgghRB9JUi2EEEIIIUQfSVIthBBCCCFEH0lSLYQQQgghRB9JUi2EEEIIIUQfSVIthBBCCCFEH0lSLYQQQgghRB9JUi2EEEIIIUQf/R9o03XY1yxH9AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 864x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_eq_kernel(x, xv, gaussian_kernel, mus, s)\n",
    "plt.suptitle(\"Gaussian Kernel\", size=15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_eq_kernel(x, xv, sigmoid_kernel, mus, s)\n",
    "plt.suptitle(\"Sigmoid Kernel\", size=15);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x1a25f34668>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 600x400 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(dpi=100)\n",
    "plt.imshow(phi_prime @ SN.T @ phi_prime.T)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
